Solving coin problems: Difference between revisions

From Rosetta Code
Content added Content deleted
m (flag for difficulty issues)
m (→‎{{header|Wren}}: Minor tidy)
 
(22 intermediate revisions by 7 users not shown)
Line 1: Line 1:
{{difficulty}}
{{difficulty}}
{{draft task|Solving coin problems}}
{{draft task}}
In 1964, Daniel G. Bobrow created the STUDENT AI program in order to solve the types of word problems found in high school algebra books. You can read Bobrow's 1964 Ph.D. thesis, ''[http://dspace.mit.edu/handle/1721.1/6903 Natural Language Input for a Computer Problem Solving System]''. The program consists of 3 main pieces:
In 1964, Daniel G. Bobrow created the STUDENT AI program in order to solve the types of word problems found in high school algebra books. You can read Bobrow's 1964 Ph.D. thesis, ''[http://dspace.mit.edu/handle/1721.1/6903 Natural Language Input for a Computer Problem Solving System]''. The program consists of 3 main pieces:
# A pattern matcher that reads the english input,
# A pattern matcher that reads the english input,
Line 28: Line 28:
The program should take coin problems written in plain english and output the solutions. The solutions needn't be output in English.
The program should take coin problems written in plain english and output the solutions. The solutions needn't be output in English.


=={{header|Perl}}==
=={{header|Go}}==
This relatively simple program can only solve problems with 2 types of coins (or other objects) or 3 types of coins (but not other objects) without the need for an equation solver. However, it is able to solve all 28 problems of these types which were originally listed in the Perl entry before it was restricted to the subset of those problems (24) involving coins and bills.
The following code reads a file containing coin problems line-by-line. It echoes comment lines starting with a hashmark and blank lines. Remaining lines are interpreted as coin problems, one per line.
<syntaxhighlight lang="go">package main


import (
The program works by matching the english input against patterns for the parts of the coin schema (a)-(e) in the task description. Patterns are expressed as perl regular expressions. It then translates these parameters into a MAXIMA program. MAXIMA is a free, open-source computer algebra system (CAS). It executes the MAXIMA script, extracts the solution, and prints it. By using perl regexes to read the input and MAXIMA to solve the resulting equations, the program may be kept fairly short.
"fmt"
"math"
"regexp"
"sort"
"strconv"
"strings"
)


type kind struct {
This program has been tested with 28 coin problems (shown below). Here is the program:
name string
<lang perl>
value float64
# coin.pl
number int
# Description: Solve math word problems involving coins.
}
# Usage: perl -CDSA coin.pl coin-problems.txt > output.txt
# Algorithm: NLP processor loosely inspired by Bobrow (1964) transforms
# english language coin problems into solvable equations that are
# piped into the Maxima computer algebra system.
# Input: File must be UTF-8 text file. One coin problem per line in english.
# Blank lines and comment lines beginning with hash mark ``#'' are OK.
# Output: STDOUT contains original problem, transformed equations and solutions.


// variable1 = constant1 * variable2 + constant2
use strict;
type relation struct {
use utf8;
variable1 string
use List::Util qw(sum);
variable2 string
use List::MoreUtils qw(uniq);
constant1 float64
constant2 float64
}


var nums = map[string]string{
our $first = 0;
"one-half": "0 times", "one": "1", "two": "2", "three": "3", "four": "4", "five": "5",
our %nums = (
"six": "6", "seven": "7", "eight": "8", "nine": "9", "ten": "10", "eleven": "11", "twelve": "12",
zero => 0, one => 1, two => 2, three => 3,
"thirteen": "13", "fourteen": "14", "fifteen": "15", "sixteen": "16", "seventeen": "17",
four => 4, five => 5, six => 6, seven => 7,
"eighteen": "18", "nineteen": "19", "twenty": "20", "thirty": "30", "forty": "40",
eight => 8, nine => 9, ten => 10, eleven => 11,
"fifty": "50", "sixty": "60", "seventy": "70", "eighty": "80", "ninety": "90",
twelve => 12, thirteen => 13, fourteen => 14, fifteen => 15,
"hundred": "100"}
sixteen => 16, seventeen => 17, eighteen => 18, nineteen => 19,
twenty => 20, thirty => 30, forty => 40, fifty => 50,
sixty => 60, seventy => 70, eighty => 80, ninety => 90,
hundred => 100, thousand => 1_000, million => 1_000_000,
billion => 1_000_000_000, trillion => 1_000_000_000_000,
# My ActiveState Win32 Perl uses e-notation after 999_999_999_999_999
quadrillion => 1e+015, quintillion => 1e+018);


var nums2 = map[string]string{
# Groupings for thousands, millions, ..., quintillions
"twenty-": "2", "thirty-": "3", "forty-": "4",
our $groups = qr/\d{4}|\d{7}|\d{10}|\d{13}|1e\+015|1e\+018/;
"fifty-": "5", "sixty-": "6", "seventy-": "7", "eighty-": "8", "ninety-": "9"}


var coins = map[string]float64{
# Numeral or e-notation
"pennies": 0.01, "nickels": 0.05, "dimes": 0.10, "quarters": 0.25, "half-dollars": 0.50,
our $num = qr/\d+|\d+e\+\d+/;
"one-dollar": 1.00, "two-dollar": 2.00, "five-dollar": 5.00, "ten-dollar": 10.00}


var bills = map[string]string{
our $float = qr/(?:(?:[1-9][0-9]*\.?[0-9]*)|(?:0?\.[0-9]+))(?:[Ee][+-]?[0-9]+)?/;
"$1": "one-dollar", "$2": "two-dollar", "$5": "five-dollar", "$10": "ten-dollar"}
our $count = 0;
our $total = 0;
our @words = ();
our @eqns = ();
our @vars = ();
our @types = ();


var (
sub add_type {
rx1 = regexp.MustCompile(`\$\d+(\.\d+)?|\d+¢`)
my ($type,$value) = @_;
rx2 = regexp.MustCompile(`\b(pennies|nickels|dimes|quarters|half-dollar|one-dollar|two-dollar|five-dollar|ten-dollar)\b`)
push @vars, "v_$type: $value";
rx3 = regexp.MustCompile(`\s(\d+)\s`)
push @types, $type;
rx4 = regexp.MustCompile(`(\d+) times as many ([-\w]+) as (s?he (does|has) )?([-\w]+)`)
rx5 = regexp.MustCompile(`(\d+) more ([-\w]+) than (s?he (does|has) )?([-\w]+)`)
rx6 = regexp.MustCompile(`(\d+) less ([-\w]+) than (s?he (does|has) )?([-\w]+)`)
rx7 = regexp.MustCompile(`(\d+) dollars`)
)

func spaced(s string) string {
return fmt.Sprintf(" %s ", s)
}
}


// Gets a sorted slice of monetary values.
while (<>) {
func getValues(q string) []float64 {
chomp; # chop trailing newline
ss := rx1.FindAllString(q, -1)
my $orig = $_;
@words = ();
if ss == nil {
return nil
@eqns = ();
@vars = ();
}
var res []float64
@types = ();
for _, s := range ss {
$count = 0;
$total = 0;
if len(s) == 0 {
continue
}
if s[0] == '$' {
s = s[1:]
} else {
s = "." + s[:len(s)-2] // '¢' is 2 bytes
}
f, _ := strconv.ParseFloat(s, 64)
res = append(res, f)
}
sort.Float64s(res)
return res
}


// Gets a sorted slice of non-monetary integers.
s/^(|)// if !$first++; # skip utf8 control seq e.g., "" that starts file
func getNumbers(q string) []int {
next if /^\s*$/; # skip blank lines
ns := rx3.FindAllString(q, -1)
# echo comment lines
if( /^\s*#.*$/ ) {
if ns == nil {
print $_, "\n";
return nil
next;
}
var res []int
}
for _, n := range ns {
s/-/ /g; # convert hyphens to spaces
i, _ := strconv.Atoi(strings.TrimSpace(n))
s/\s\s+/ /g; # remove duplicate whitespace, convert ws to space
res = append(res, i)
s/ $//g; # remove trailing blank
}
s/^ //g; # remove leading blank
sort.Ints(res)
$_ = lc($_); # convert to lower case
return res
# tokenize sentence boundaries
}
s/([\.\?\!]) / $1\n/g;
s/([\.\?\!])$/ $1\n/g;
# tokenize other punctuation and symbols
s/\$(.)/\$ $1/g; # prefix
s/(.)([\;\:\%',¢])/$1 $2/g; # suffix
s/\btwice\b/two times/g;
# Fractions
s/half.dollar(s?)/half_dollar/g;
s/\bone half\b/0.5/g;
s/\bhalf\b/0.5/g;


// Gets the 'kinds' for the problem.
# Remove noise words
func getKinds(a []string) (int, []kind) {
s/\b(the|a|to|of|i|is|that|it|on|you|this|for|but|with|are|have|be|at|or|was|so|if|out|not|he|she|they|has|do|does)\b\s*//g;
num, _ := strconv.Atoi(a[1])
kinds := []kind{{a[2], 0, 0}, {a[5], 0, 0}}
areCoins := false
for i := range kinds {
if v, ok := coins[kinds[i].name]; ok {
kinds[i].value = v
areCoins = true
}
}
if !areCoins {
return 0, nil
}
return num, kinds
}


// Checks if the problem involves 3 coins and
# Convert English number-names to numbers
// also returns their names and the names of the coin which occurs most.
foreach my $key (keys %nums) { s/\b$key\b/$nums{$key}/eg; }
func hasThreeCoins(q string) ([]string, []string, bool) {
q = strings.ReplaceAll(q, ".", "")
q = strings.ReplaceAll(q, ",", "")
words := strings.Split(q, " ")
coinMap := make(map[string]int)
for _, word := range words {
if _, ok := coins[word]; ok {
coinMap[word]++
}
}
if len(coinMap) != 3 {
return nil, []string{}, false
}
maxNum := 0
var maxNames []string
var names []string
for k, v := range coinMap {
names = append(names, k)
if v > maxNum {
maxNum = v
maxNames = maxNames[:0]
maxNames = append(maxNames, k)
} else if v == maxNum {
maxNames = append(maxNames, k)
}
}
return names, maxNames, true
}


// Processes a problem which involves 3 coins.
s/(\d) , (\d)/$1 $2/g;
func threeCoins(p, q string, names, maxNames []string) {
s/(\d) and (\d)/$1 $2/g;
var relations []relation
am := rx4.FindAllStringSubmatch(q, -1)
for i := 0; i < len(am); i++ {
mult, kinds := getKinds(am[i])
relations = append(relations, relation{kinds[0].name, kinds[1].name, float64(mult), 0})
}
mt := rx5.FindAllStringSubmatch(q, -1)
for i := 0; i < len(mt); i++ {
plus, kinds := getKinds(mt[i])
relations = append(relations, relation{kinds[0].name, kinds[1].name, 1, float64(plus)})
}
lt := rx6.FindAllStringSubmatch(q, -1)
for i := 0; i < len(lt); i++ {
minus, kinds := getKinds(lt[i])
relations = append(relations, relation{kinds[0].name, kinds[1].name, 1, -float64(minus)})
}
le := len(relations)
if le > 2 {
errorMsg(p)
return
}
if le == 0 { // numbers of each coin must be the same
sum := 0.0
for _, name := range names {
sum += coins[name]
}
res := getValues(q)
tv := res[len(res)-1]
n := int(tv/sum + 0.5)
var kinds []kind
for _, name := range names {
kinds = append(kinds, kind{name, 0, n})
}
printAnswers(p, kinds)
} else {
res := getValues(q)
totalValue := res[len(res)-1]
for _, maxName := range maxNames {
for i := 0; i < le; i++ {
if relations[i].constant1 == 0 {
relations[i].constant1 = 0.5 // deals with 'one-half' cases
}
if le == 2 && maxName == relations[i].variable1 {
v := relations[i].variable2
relations[i].variable1, relations[i].variable2 = v, maxName
relations[i].constant1 = 1 / relations[i].constant1
relations[i].constant2 = -relations[i].constant2
}
}
tv := totalValue
var v1, v2, v3 string
var n1, n2, n3 int
if le == 2 {
tmc := coins[relations[0].variable1]*relations[0].constant1 +
coins[relations[1].variable1]*relations[1].constant1 + coins[maxName]
tv -= coins[relations[0].variable1]*relations[0].constant2 +
coins[relations[1].variable1]*relations[1].constant2
v1, v2, v3 = maxName, relations[0].variable1, relations[1].variable1
n1 = int(tv/tmc + 0.5)
n2 = int(relations[0].constant1*float64(n1) + relations[0].constant2 + 0.5)
n3 = int(relations[1].constant1*float64(n1) + relations[1].constant2 + 0.5)
} else {
res2 := getNumbers(q)
tn := float64(res2[len(res2)-1])
v1, v2 = relations[0].variable1, relations[0].variable2
for _, name := range names {
if name != v1 && name != v2 {
v3 = name
break
}
}
mult1, mult2, mult3 := coins[v1], coins[v2], coins[v3]
n2 = int(((tn-relations[0].constant2)*mult3-tv+relations[0].constant2*mult1)/
((relations[0].constant1+1)*mult3-relations[0].constant1*mult1-mult2) + 0.5)
n1 = int(float64(n2)*relations[0].constant1 + relations[0].constant2 + 0.5)
n3 = int(tn) - n1 - n2
}
calcValue := float64(n1)*coins[v1] + float64(n2)*coins[v2] + float64(n3)*coins[v3]
if math.Abs(totalValue-calcValue) <= 1e-14 {
kinds := []kind{kind{v1, 0, n1}, kind{v2, 0, n2}, kind{v3, 0, n3}}
printAnswers(p, kinds)
return
}
}
errorMsg(p)
}
return
}


func printAnswers(p string, kinds []kind) {
s/\b(\d) 100 (\d\d) (\d) (${groups})\b/($1 * 100 + $2 + $3) * $4/eg;
fmt.Println(p)
fmt.Print("ANSWER:")
for i, kind := range kinds {
if i > 0 {
fmt.Print(",")
}
fmt.Printf(" %d %s", kind.number, kind.name)
}
fmt.Println("\n")
}


func errorMsg(p string) {
s/\b(\d) 100 (\d\d) (${groups})\b/($1 * 100 + $2) * $3/eg;
fmt.Println(p)
s/\b(\d) 100 (\d) (${groups})\b/($1 * 100 + $2) * $3/eg;
fmt.Println("*** CAN'T SOLVE THIS ONE ***\n")
s/\b(\d) 100 (${groups})\b/$1 * $2 * 100/eg;
}


func main() {
s/\b100 (\d\d) (\d) (${groups})\b/(100 + $1 + $2) * $3/eg;
ps := []string{
s/\b100 (\d\d) (${groups})\b/(100 + $1) * $2/eg;
"If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.",
s/\b100 (\d) (${groups})\b/(100 + $1) * $2/eg;
"A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.",
s/\b100 (${groups})\b/$1 * 100/eg;
"A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.",
"A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.",
"A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.",
"In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.",
"A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.",
"A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.",
"An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?",
"A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?",
"A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?",
"A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?",
"A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.",
"A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.",
"A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.",
"A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.",
"Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?",
"A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?",
"A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?",
"Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?",
"Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?",
"In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?",
"Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?",
"A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?",
"Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?",
"Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?",
"Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?",
"A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?",
}
for _, p := range ps {
q := strings.ToLower(p)
q = strings.ReplaceAll(q, "twice", "two times")
for _, d := range []string{"half", "one", "two", "five", "ten"} {
q = strings.ReplaceAll(q, d+" dollar", d+"-dollar")
}
for k, v := range nums {
q = strings.ReplaceAll(q, spaced(k), spaced(v))
}
for k, v := range nums2 {
q = strings.ReplaceAll(q, k, v)
}
for k, v := range nums {
q = strings.ReplaceAll(q, k+" ", v+" ")
}
for k, v := range bills {
q = strings.ReplaceAll(q, k+" ", v+" ")
}
q = strings.ReplaceAll(q, " bills", "")
q = strings.ReplaceAll(q, " bill", "")
// check if there are 3 coins involved
if names, maxNames, ok := hasThreeCoins(q); ok {
threeCoins(p, q, names, maxNames)
continue
}
am := rx4.FindAllStringSubmatch(q, -1)
if len(am) == 1 {
mult, kinds := getKinds(am[0])
if kinds == nil {
errorMsg(p)
continue
}
res := getValues(q)
tv := res[len(res)-1]
fmult := float64(mult)
kinds[1].number = int(tv/(fmult*kinds[0].value+kinds[1].value) + 0.5)
kinds[0].number = kinds[1].number * mult
printAnswers(p, kinds)
continue
}
mt := rx5.FindAllStringSubmatch(q, -1)
if len(mt) == 1 {
plus, kinds := getKinds(mt[0])
if kinds == nil {
errorMsg(p)
continue
}
res := getValues(q)
tv := res[len(res)-1]
fplus := float64(plus)
kinds[1].number = int((tv-fplus*kinds[0].value)/(kinds[0].value+kinds[1].value) + 0.5)
kinds[0].number = kinds[1].number + plus
printAnswers(p, kinds)
continue
}
lt := rx6.FindAllStringSubmatch(q, -1)
if len(lt) == 1 {
minus, kinds := getKinds(lt[0])
if kinds == nil {
errorMsg(p)
continue
}
res := getValues(q)
tv := res[len(res)-1]
fminus := float64(minus)
kinds[1].number = int((tv+fminus*kinds[0].value)/(kinds[0].value+kinds[1].value) + 0.5)
kinds[0].number = kinds[1].number - minus
printAnswers(p, kinds)
continue
}
res := getValues(q)
var tv float64
if len(res) > 0 {
tv = res[len(res)-1]
} else {
res3 := rx7.FindAllStringSubmatch(q, -1)
i, _ := strconv.Atoi(res3[0][1])
tv = float64(i)
}
res2 := getNumbers(q)
tn := res2[len(res2)-1]
coinNames := rx2.FindAllString(q, -1)
sort.Strings(coinNames)
var kinds []kind
if len(coinNames) > 0 {
kinds = append(kinds, kind{coinNames[0], coins[coinNames[0]], 0})
for i := 1; i < len(coinNames); i++ {
if coinNames[i] != coinNames[i-1] {
kinds = append(kinds, kind{coinNames[i], coins[coinNames[i]], 0})
}
}
if len(kinds) != 2 {
errorMsg(p)
continue
}
} else if len(res) >= 3 {
kinds = append(kinds, kind{fmt.Sprintf("$%.2f item", res[0]), res[0], 0})
for i := 1; i < len(res)-1; i++ {
if res[i] != res[i-1] {
kinds = append(kinds, kind{fmt.Sprintf("$%.2f item", res[i]), res[i], 0})
}
}
if len(kinds) != 2 {
errorMsg(p)
continue
}
} else {
errorMsg(p)
continue
}
ftn := float64(tn)
kinds[0].number = int((tv-ftn*kinds[1].value)/(kinds[0].value-kinds[1].value) + 0.5)
kinds[1].number = tn - kinds[0].number
printAnswers(p, kinds)
}
}</syntaxhighlight>


{{out}}
s/\b(\d\d) (\d) (${groups})\b/($1 + $2) * $3/eg;
<pre>
s/\b(\d{1,2}) (${groups})\b/$1 * $2/eg;
If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.
ANSWER: 21 quarters, 7 dimes


A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.
s/\b(\d\d) (\d) 100\b/($1 + $2) * 100/eg;
ANSWER: 5 nickels, 13 pennies
s/\b(\d{1,2}) 100\b/$1 * 100/eg;


A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.
# anomolous cases: nineteen eighty-four and twenty thirteen
ANSWER: 11 quarters, 5 nickels
s/\b(\d{2}) (\d{2})\b/$1 * 100 + $2/eg;


A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.
s/((?:${num} )*${num})/sum(split(" ",$1))/eg;
ANSWER: 21 nickels, 11 quarters


A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
s/dollar coin/dollar_coin/g;
ANSWER: 7 pennies, 14 dimes, 10 nickels
s/quarters/quarter/g;
s/dimes/dime/g;
s/nickels/nickel/g;
s/pennies/penny/g;
s/dollars/dollar/g;
s/coins/coin/g;
s/bills/bill/g;
s/(\d+) dollar\b/\$ $1/g;


In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.
# Rules for coin problems
ANSWER: 3 half-dollars, 9 quarters, 9 dimes
# Rule triggers are just regexes


A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.
add_type("dollar_coin",100) if /dollar_coin/;
ANSWER: 5 $0.23 item, 7 $0.37 item
add_type("half_dollar",50) if /half_dollar/;
add_type("quarter",25) if /quarter/;
add_type("dime",10) if /dime/;
add_type("nickel",5) if /nickel/;
add_type("penny",1) if /penny/;


A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.
while(/(${float}) (?:times )?as many \$ (\d+) bill as \$ (\d+) bill/g) {
ANSWER: 32 $0.69 item, 48 $0.75 item
push @eqns, "n_$2 = $1 * n_$3";
}


An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?
while(/(${float}) (?:times )?as many (\w+) as (\w+)/g) {
ANSWER: 7 $1.59 item, 2 $2.29 item
push @eqns, "n_$2 = $1 * n_$3";
}


A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?
while(/(\d+) more (\w+) than (\w+)/g) {
ANSWER: 5 five-dollar, 10 one-dollar, 4 ten-dollar
push @eqns, "n_$2 = n_$3 + $1";
}


A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?
while(/(\d+) less (\w+) than (\w+)/g) {
ANSWER: 5 dimes, 3 quarters
push @eqns, "n_$2 = n_$3 - $1";
}


A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?
if(/same number (\w+) , (\w+) (?:, )?and (\w+)/){
ANSWER: 3 nickels, 9 dimes, 8 pennies
push @eqns, "n_$1 = n_$2";
push @eqns, "n_$2 = n_$3";
} elsif(/same number (\w+) and (\w+)/){
push @eqns, "n_$1 = n_$2";
}


A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.
if(/(\d+) (?:\w+ )*?consists/
ANSWER: 6 $1.50 item, 4 $2.00 item
or /(\d+) (?:\w+ )*?,?consisting/
or /total (\d+)(?! ¢)/
or /(?<!\$ )(\d+) coin/
or /[^\$] (\d+) bill/
or /number [^\?\!\.0-9]*?(\d+)/) {
$count = $1;
push @vars, "count: $count";
}


A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.
if(/total (?:\w+ )*?\$ (${float})/
ANSWER: 11 dimes, 2 nickels
or /valu(?:e|ing) \$ (${float})/

or /\$ (${float}) ((bill|coin) )?in/) {
A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.
$total = 100 * $1;
ANSWER: 5 one-dollar, 15 two-dollar
push @vars, "total: $total";

}
A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
ANSWER: 17 nickels, 25 pennies, 20 dimes

Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
ANSWER: 14 one-dollar, 12 quarters

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
ANSWER: 18 nickels, 6 quarters, 9 dimes

A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
ANSWER: 9 pennies, 9 nickels, 9 dimes

Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
ANSWER: 8 dimes, 17 nickels

Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
ANSWER: 20 quarters, 18 dimes

In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?
ANSWER: 8 one-dollar, 2 ten-dollar, 3 five-dollar

Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?
ANSWER: 12 one-dollar, 4 five-dollar

A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?
ANSWER: 90 dimes, 45 nickels, 120 quarters

Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?
ANSWER: 15 dimes, 12 quarters

Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?
ANSWER: 140 nickels, 25 quarters

Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?
ANSWER: 121 quarters, 150 dimes

A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
ANSWER: 2 dimes, 10 pennies
</pre>

=={{header|Julia}}==
Uses the JuMP optimization library as a solver. The examples are from the Go code, and a few regex are from the Perl code.
<syntaxhighlight lang="julia">using JuMP, GLPK

const nums = Dict(
"zero" => 0, "one" => 1, "two" => 2, "three" => 3,
"four" => 4, "five" => 5, "six" => 6, "seven" => 7,
"eight" => 8, "nine" => 9, "ten" => 10, "eleven" => 11,
"twelve" => 12, "thirteen" => 13, "fourteen" => 14, "fifteen" => 15,
"sixteen" => 16, "seventeen" => 17, "eighteen" => 18, "nineteen" => 19,
"twenty" => 20,
)

function coinproblemsolver(text, maxitems=4, verbose=false)
coin_problem = Model(GLPK.Optimizer)
for line in strip.(split(text, r"\n\n"))

# save original version
oldline = deepcopy(line)

# ignore short or commented lines
length(line) < 5 && continue
line[1] == '#' && continue

# create the data structures and registration function
monies = Dict(
"dollar_coin" => 100, "half_dollar" => 50, "quarter" => 25, "dime" => 10,
"nickel" => 5, "penny" => 1,
)
foreach(d -> (monies["_" * "$d" * "_bill"] = 100 * d), [1, 2, 5, 10, 20, 50, 100, 500, 1000])

itemnames = String[]
itemvalues = Int[]

function register_variables(vars)
indices = Int[]
for cap in vars
idx = findfirst(x -> cap == x, itemnames)
if !(idx isa Nothing)
push!(indices, idx)
else
push!(itemnames, cap)
push!(indices, length(itemnames))
push!(itemvalues, get(monies, cap, 0))
end
end
return indices
end


# set up the optimizer / problem solver
@variables(coin_problem, begin x[1:maxitems] >= 0 end)


# Simplify sentence and standardize quantities

# convert hyphens to spaces, lowercase, newlines to spaces
line = replace(replace(lowercase(line), "-" => " "), "\n" => " ")

# fractions/multipliers to parsable forms
line = replace(line, r"half.dollars?" => "half_dollar")
line = replace(line, r"\bone\s+half\b" => "0.5")
line = replace(line, r"\btwice\b" => "two times")

# convert spelled out number to integer text per nums dictionary
for p in nums
line = replace(line, Regex("\\b" * p[1] * "\\b") => string(p[2]))
end

# remove plurals of coinage
line = replace(line, r"(quarter|dime|nickel|dollar|coin|bill)s" => s"\1")
line = replace(line, "pennies" => "penny")

# change numerals to quantites and monies
line = replace(line, r"dollar coin|all dollar" => "dollar_coin")
line = replace(line, r"\$(\d+) bill" => s"_\1_bill")
line = replace(line, r"(\d+) dollar bill" => s"_\1_bill")
line = replace(line, r"((?:\d+\s+)+\d+)" => (s) -> mapreduce(x -> parse(Int, x), +, split(s))) # 20 6 -> 26

# remove most unparsed words
line = replace(line, r"\b(the|a|to|of|i|is|that|it|on|you|this|for|but|with|are|have|be|at|or|was|so|if|out|not|he|she|they|has|do|did|does)\b" => "")
# simplify spacing
line = replace(line, r"\s+" => " ")

# Add variables and constraints to the problem
for m in eachmatch(r"([\d\.]+) (?:times )?as many (\w+) as (\w+)", line)
indices = register_variables([m[2], m[3]])
@constraints(coin_problem, begin x[indices[1]] == x[indices[2]] * parse(Float64, m[1]) end)
end
for m in eachmatch(r"(\d+) more (\w+) than (\w+)", line)
indices = register_variables([m[2], m[3]])
@constraints(coin_problem, begin x[indices[1]] == x[indices[2]] + parse(Int, m[1]) end)
end
for m in eachmatch(r"(\d+) less (\w+) than (\w+)", line)
indices = register_variables([m[2], m[3]])
@constraints(coin_problem, begin x[indices[1]] == x[indices[2]] - parse(Int, m[1]) end)
end
if (m = match(r"same number (\w+), (\w+),? and (\w+)", line)) != nothing
indices = register_variables(m.captures)
@constraints(coin_problem, begin
x[indices[1]] == x[indices[2]]
x[indices[2]] == x[indices[3]]
end)
end
if (m = match(r"(\d+) (?:\w+ )?(\w+),? consist\D+\$([\d\.]+)\D+\$([\d\.]+)", line)) != nothing
n1, n2 = Int(round(100 * parse(Float64, m[3]))), Int(round(100 * parse(Float64, m[4])))
s1, s2 = m[2] * "_costing_" * string(n1), m[2] * "_costing_" * string(n2)
monies[s1], monies[s2] = n1, n2
indices = register_variables([s1, s2])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(\d+) (?:\w+ )?(\w+),? consist\D+([\d\.]+)¢\D+([\d\.]+)¢", line)) != nothing
n1, n2 = parse(Int, m[3]), parse(Int, m[4])
s1, s2 = m[2] * "_costing_" * string(n1), m[2] * "_costing_" * string(n2)
monies[s1], monies[s2] = n1, n2
indices = register_variables([s1, s2])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(\d+) (?:coin|bill),? consist(?:s|ing) (\w+) and (\w+)", line)) != nothing
indices = register_variables([m[2], m[3]])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(\d+) (?:coin)[^\d\.,]+pocket (\w+) and (\w+)", line)) != nothing
indices = register_variables([m[2], m[3]])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(\d+) (?:coin|bill),? consist(?:s|ing) (\w+), (\w+), and (\w+)", line)) != nothing
indices = register_variables([m[2], m[3], m[4]])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"\$([\d\.]+) ream\D+\$([\d\.]+)\D+(\d+) reams", line)) != nothing
n1, n2 = Int(round(100 * parse(Float64, m[1]))), Int(round(100 * parse(Float64, m[2])))
s1, s2 = "ream_costing_" * string(n1), "ream_costing_" * string(n2)
monies[s1], monies[s2] = n1, n2
indices = register_variables([s1, s2])
@constraints(coin_problem, begin sum(x) == parse(Int, m[3]) end)
end
if (m = match(r"(?:in my wallet,?|only accepts) (\w+), (\w+),? and (\w+)", line)) != nothing
indices = register_variables([m.captures[1], m.captures[2], m.captures[3]])
end
if (m = match(r"(\d+) coin in (\w+) and (\w+) only", line)) != nothing
indices = register_variables([m.captures[2], m.captures[3]])
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(\d+) coin (?:total|in all)", line)) != nothing
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
if (m = match(r"(?:had only|in) (\w+) and (\w+)[,\.\?]", line)) != nothing
indices = register_variables([m.captures[1], m.captures[2]])
end
if (m = match(r"(?:sold total|all together,? there) (\d+)", line)) != nothing
@constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
end
for m in eachmatch(r"cost \$([\d\.]+) each", line)
s = "item_costing_" * m.captures[1]
monies[s] = Int(round(100 * parse(Float64, m.captures[1])))
register_variables([s])
end

# find a total
m = match(r"add up \$?([\d\.]+)", line)
if m isa Nothing
m = match(r"(?:cost stamps|total cost|paid|value|valuing|store made)[^\$]+\$([\d\.]+)", line)
end
if m isa Nothing
m = match(r"(?:total|value of|store made|given)[^\$]+\$([\d\.]+)", line)
end
if m isa Nothing
m = match(r"\$([\d\.]+) (?:coin )?in", line)
end
if !(m isa Nothing)
m1 = m.captures[1][end] == '.' ? m.captures[1][1:end-1] : m.captures[1]
@constraints(coin_problem, begin
sum([itemvalues[i] * x[i] for i in 1:length(itemnames)]) == Int(round(100 * parse(Float64, m1)))
end)
else
m = match(r"total (?:amount coin )([\d\.]+)¢", line)
if !(m isa Nothing)
@constraints(coin_problem, begin
sum([itemvalues[i] * x[i] for i in 1:length(itemnames)]) == parse(Int, m[1])
end)
else
error("Missing or unparsed total funds constraint")
end
end


# set unused x components to 0
for i in length(itemnames)+1:maxitems
@constraints(coin_problem, begin x[i] == 0 end)
end

# solve
optimize!(coin_problem)
verbose && println(line)
verbose && println(coin_problem)
print(oldline, "\nAnswer: ")
for i in eachindex(itemnames)
print(rpad(itemnames[i] * "(s)", 10), ": ", rpad(Int(round(JuMP.value(x[i]))), 10))
end
println("\n")
JuMP.empty!(coin_problem)
end
end

const DATA = raw"""
If a person has three times as many quarters as dimes and the total amount of money is $5.95,
find the number of quarters and dimes.

A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢,
find the number of pennies and nickels.

A small child has 6 more quarters than nickels. If the total amount of coins is $3.00,
find the number of nickels and quarters the child has.

A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of
money is $3.80, find the number of nickels and quarters in the bank.

A person has twice as many dimes as she has pennies and three more nickels than pennies. If
the total amount of the coins is $1.97, find the numbers of each type of coin the person has.

In a bank, there are three times as many quarters as half dollars and 6 more dimes than
half dollars. If the total amount of the money in the bank is $4.65, find the number of
each type of coin in the bank.

A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps
is $3.74, find the number of each type of the stamps purchased.

A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches
cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number
of each sold.

An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled
notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and
paid $15.71, how many reams of each type of paper did the student purchase?

A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are
twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each
type of bill are there?

A person has 8 coins consisting of quarters and dimes. If the total amount of this change
is $1.25, how many of each kind of coin are there?

A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the
total amount of these coins is $1.13, how many of each kind of coin does he have?

A person bought ten greeting cards consisting of birthday cards costing $1.50 each and
anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the
number of each kind of card the person bought.

A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the
number of dimes the person has.

A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money
the person has is $35, find the number of $2 bills the person has.

A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total
amount of money in the bank is $3.10, find the number of dimes in the bank.

Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you
can have all the coins if you can figure out how many of each kind of coin he is carrying.
You're not too interested until he tells you that he's been collecting those gold-tone
one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they
add up to seventeen dollars in value. How many of each coin does he have?

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30.
If there are three times as many nickels as quarters, and one-half as many dimes as nickels,
how many coins of each kind are there?

A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How
many of each type of coin does the wallet contain?

Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of
each coin does he have?

Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes
is 38. How many quarters and dimes does Terry have?

In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total
amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills.
All together, there are 13 bills in my wallet. How many of each bill do I have?

Marsha has three times as many one-dollar bills as she does five dollar bills. She has a
total of $32. How many of each bill does she have?

A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts
nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin
are in the machine?

Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins
of each kind did he have?

Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each
type of coin did she have?

Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each
type of coin does he have?

A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30,
how many of each coin are there?
"""

coinproblemsolver(DATA)

</syntaxhighlight>{{out}}
<pre>
If a person has three times as many quarters as dimes and the total amount of money is $5.95,
find the number of quarters and dimes.
Answer: quarter(s): 21 dime(s) : 7

A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢,
find the number of pennies and nickels.
Answer: penny(s) : 13 nickel(s) : 5

A small child has 6 more quarters than nickels. If the total amount of coins is $3.00,
find the number of nickels and quarters the child has.
Answer: quarter(s): 11 nickel(s) : 5

A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of
money is $3.80, find the number of nickels and quarters in the bank.
Answer: nickel(s) : 21 quarter(s): 11

A person has twice as many dimes as she has pennies and three more nickels than pennies. If
the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
Answer: dime(s) : 14 penny(s) : 7 nickel(s) : 10

In a bank, there are three times as many quarters as half dollars and 6 more dimes than
half dollars. If the total amount of the money in the bank is $4.65, find the number of
each type of coin in the bank.
Answer: quarter(s): 9 half_dollar(s): 3 dime(s) : 9

A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps
is $3.74, find the number of each type of the stamps purchased.
Answer: stamps_costing_37(s): 7 stamps_costing_23(s): 5

A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches
cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number
of each sold.
Answer: item_costing_0.69(s): 32 item_costing_0.75(s): 48

An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled
notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and
paid $15.71, how many reams of each type of paper did the student purchase?
Answer: ream_costing_159(s): 7 ream_costing_229(s): 2

A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are
twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each
type of bill are there?
Answer: _1_bill(s): 10 _5_bill(s): 5 _10_bill(s): 4

A person has 8 coins consisting of quarters and dimes. If the total amount of this change
is $1.25, how many of each kind of coin are there?
Answer: quarter(s): 3 dime(s) : 5

A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the
total amount of these coins is $1.13, how many of each kind of coin does he have?
Answer: dime(s) : 9 nickel(s) : 3 penny(s) : 8

A person bought ten greeting cards consisting of birthday cards costing $1.50 each and
anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the
number of each kind of card the person bought.
Answer: cards_costing_150(s): 6 cards_costing_200(s): 4

A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the
number of dimes the person has.
Answer: dime(s) : 11 nickel(s) : 2

A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money
the person has is $35, find the number of $2 bills the person has.
Answer: _1_bill(s): 5 _2_bill(s): 15

A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total
amount of money in the bank is $3.10, find the number of dimes in the bank.
Answer: penny(s) : 25 nickel(s) : 17 dime(s) : 20

Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you
can have all the coins if you can figure out how many of each kind of coin he is carrying.
You're not too interested until he tells you that he's been collecting those gold-tone
one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they
add up to seventeen dollars in value. How many of each coin does he have?
Answer: dollar_coin(s): 14 quarter(s): 12

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30.
If there are three times as many nickels as quarters, and one-half as many dimes as nickels,
how many coins of each kind are there?
Answer: nickel(s) : 18 quarter(s): 6 dime(s) : 9

A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How
many of each type of coin does the wallet contain?
Answer: penny(s) : 9 nickel(s) : 9 dime(s) : 9

Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of
each coin does he have?
Answer: nickel(s) : 17 dime(s) : 8

Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes
is 38. How many quarters and dimes does Terry have?
Answer: quarter(s): 20 dime(s) : 18

In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total
amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills.
All together, there are 13 bills in my wallet. How many of each bill do I have?
Answer: _1_bill(s): 8 _10_bill(s): 2 _5_bill(s): 3

Marsha has three times as many one-dollar bills as she does five dollar bills. She has a
total of $32. How many of each bill does she have?
Answer: _1_bill(s): 12 _5_bill(s): 4

A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts
nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin
are in the machine?
Answer: dime(s) : 90 nickel(s) : 45 quarter(s): 120

Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins
of each kind did he have?
Answer: quarter(s): 12 dime(s) : 15

Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each
type of coin did she have?
Answer: nickel(s) : 140 quarter(s): 25

Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each
type of coin does he have?
Answer: quarter(s): 121 dime(s) : 150

A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30,
how many of each coin are there?
Answer: dime(s) : 2 penny(s) : 10
</pre>

=={{header|Perl}}==
Coin-type 'word problems' are analyzed into their constituent algebraic relationships, in a format suitable for processing by MAXIMA, a free computer algebra system. NB: MAXIMA <b>must</b> be locally installed for this task to function.
<syntaxhighlight lang="perl">use strict;
use warnings;


use List::Util qw(sum uniq);
if(/total (?:\w+ )*?(${float}) ¢/) {
use File::Temp qw(tempfile);
$total = $1;
push @vars, "total: $total";
}


my %nums = (
# Rules for stamp problems
zero => 0, one => 1, two => 2, three => 3,
s/stamps/stamp/g;
four => 4, five => 5, six => 6, seven => 7,
while(/(\d+) ¢ stamp/g) { add_type("$1_stamp", $1); }
eight => 8, nine => 9, ten => 10, eleven => 11,
if(/cost (?:\w+ )*?\$ (${float}) (?!each)/) { $total = 100 * $1; push @vars, "total: $total"; }
twelve => 12, thirteen => 13, fourteen => 14, fifteen => 15,
sixteen => 16, seventeen => 17, eighteen => 18, nineteen => 19,
twenty => 20,
);


my $decimal = qr/(?:[1-9][0-9]*\.?[0-9]*)|(?:0?\.[0-9]+)/;
# Rules for unusual types
while(/(\w+) cost \$ (${float}) each/g) { add_type($1, 100 * $2); }
if(/made \$ (${float})/) { $total = 100 * $1; push @vars, "total: $total"; }


while (<DATA>) {
# Rules for bill problems
chomp;
while(/\$ (\d+) bill/g) { add_type($1, 100 * $1); }
next if /^\s*$/ or /^\s*#.*$/; # skip blank and comment lines
while(/(\d+) times as many \$ (\d+) bill as \$ (\d+) bill/g) { push @eqns, "n_$2 = $1 * n_$3"; }
while(/(\d+) more \$ (\d+) bill than \$ (\d+) bill/g) { push @eqns, "n_$2 = n_$3 + $1"; }
while(/(\d+) less \$ (\d+) bill than \$ (\d+) bill/g) { push @eqns, "n_$2 = n_$3 - $1"; }
if(/\$ (${float}) in bill/) { $total = 100 * $1; push @vars, "total: $total"; }


my($count, $total) = (0, 0);
# Rules for greeting card example
our @words = our @eqns = our @vars = our @types = ();
if(/consisting (.+?)costing \$ (${float}) each and (.+?)costing \$ (${float}) each/) {
my ($t1,$v1,$t2,$v2) = ($1,$2,$3,$4);
$t1 =~ s/ $//; $t1 =~ s/ /_/g;
$t2 =~ s/ $//; $t2 =~ s/ /_/g;
add_type($t1,100*$v1);
add_type($t2,100*$v2);
}


sub add_type {
# Rules for notebook paper example
my($type,$value) = @_;
if(/sells ([^\$]+)\$ (${float}) (\w+) and ([^\$]+)\$ (${float}) (\w+)/) {
push @vars, "v_$type: $value";
my ($t1,$v1,$u1,$t2,$v2,$u2) = ($1,$2,$3,$4,$5,$6);
$t1 =~ s/ $//; $t1 =~ s/ /_/g;
push @types, $type;
$t2 =~ s/ $//; $t2 =~ s/ /_/g;
add_type($t1,100*$v1);
add_type($t2,100*$v2);
if($u1 eq $u2){
if(/purchased (\d+) ${u1}(?:s|es)? (?:\w+ )*?and paid \$ (${float})/){
$count = $1; push @vars, "count: $count";
$total = 100*$2; push @vars, "total: $total";
}
}
}
}


# Step 1: standardize language
# Rules ALL coin problems obey...
# Rule no 1: Total is sum over all coin types of coin value times coin number
# i.e., total = dot product of values and quantities
my $dot = join(" + ", map {"n_$_ * v_$_"} uniq @types);
if($total && scalar @types){ push @eqns, "total = $dot"; }


s/-/ /g; # convert hyphens to spaces
# Rule no 2: Count of all coins is sum of counts of each coin type
$_ = lc($_); # convert to lower case
my $trace = join(" + ", map {"n_$_"} uniq @types);
if($count && scalar @types){ push @eqns, "count = $trace"; }


# tokenize sentence boundaries, punctuation, symbols
print "original input: $orig\n";
s/([\.\?\!]) / $1\n/g;
s/([\.\?\!])$/ $1\n/g;
s/\$(.)/\$ $1/g; # prefix
s/(.)([\;\:\%',¢])/$1 $2/g; # suffix


# fractions/multipliers
# Prepare MAXIMA batch file
s/half.dollars?/half_dollar/g;
my $maxima_vars = join("\$\n", uniq @vars);
s/\b(one )?half\b/0.5/g;
my $maxima_eqns = "[". join(", ", @eqns) . "]";
s/\btwice\b/two times/g;
my $maxima_find = "[". join(", ", map {"n_$_"} @types) . "]";

my $maxima_script = "${maxima_vars}\$\nsolve(${maxima_eqns}, ${maxima_find});\n";
# convert English number-names to numbers
print $maxima_script;
foreach my $key (keys %nums) { s/\b$key\b/$nums{$key}/eg }
if(scalar @eqns && scalar @vars) {

my $temp = time() . "_" . rand() . ".max";
# remove plurals
open(TEMP, ">$temp") || die "Couldn't open temp file: $!\n";
s/(quarter|dime|nickel|dollar|coin|bill)s/$1/g;
print TEMP $maxima_script;
close TEMP;
s/pennies/penny/g;

open(MAXIMA, "maxima -q -b $temp |") || die "Couldn't open maxima: $!\n";
while(<MAXIMA>) {
# misc
s/dollar coin/dollar_coin/g;
# filter out everything but output line with the solution
if(/\(\%o\d+\)\s+\[\[([^\]]+)\]\]/) {
s/(\d+) dollar\b/\$ $1/g;
s/((?:\d+ )*\d+)/sum(split(' ',$1))/eg;
print "solution: $1\n";

}
# remove non-essential words
s/\b(the|a|to|of|i|is|that|it|on|you|this|for|but|with|are|have|be|at|or|was|so|if|out|not|he|she|they|has|do|did|does)\b\s*//g;

# Step 2: assign numeric values to terms

add_type('dollar_coin',100) if /dollar_coin/;
add_type('half_dollar',50) if /half_dollar/;
add_type('quarter',25) if /quarter/;
add_type('dime',10) if /dime/;
add_type('nickel',5) if /nickel/;
add_type('penny',1) if /penny/;
add_type($1, 100 * $1) while /\$ (\d+) bill/g;

# Step 3: determine algebraic relationships

while (/($decimal) (?:times )?as many \$ (\d+) bill as \$ (\d+) bill/g) { push @eqns, "n_$2 = n_$3 * $1" }
while (/($decimal) (?:times )?as many (\w+) as (\w+)/g) { push @eqns, "n_$2 = n_$3 * $1" }
while (/(\d+) more (\w+) than (\w+)/g) { push @eqns, "n_$2 = n_$3 + $1" }
while (/(\d+) less (\w+) than (\w+)/g) { push @eqns, "n_$2 = n_$3 - $1" }
while (/(\d+) less \$ (\d+) bill than \$ (\d+) bill/g) { push @eqns, "n_$2 = n_$3 - $1" }

if (/same number (\w+) , (\w+) (?:, )?and (\w+)/) {
push @eqns, "n_$1 = n_$2";
push @eqns, "n_$2 = n_$3";
}

if (/(\d+) (?:\w+ )*consists/ or /(?<!\$ )(\d+) coin/ or /[^\$] (\d+) bill/) {
$count = $1; push @vars, "count: $count"
}

if (/total (?:\w+ )*\$ ($decimal)/ or /valu(?:e|ing) \$ ($decimal)/ or /\$ ($decimal) ((bill|coin) )?in/) {
$total = 100 * $1;
push @vars, "total: $total";
}

if (/total (?:\w+ )*($decimal)/) {
$total = $1;
push @vars, "total: $total";
}

# Step 4: tally final total value, coin count

# sum total, dot product of values and quantities
my $dot_product = join(' + ', map {"n_$_ * v_$_"} uniq @types);
push @eqns, "total = $dot_product" if $total and @types;

# count of all coins, sum of counts of each coin type
my $trace = join(' + ', map {"n_$_"} uniq @types);
push @eqns, "count = $trace" if $count and @types;

# Step 5: prepare batch file for external processing, run 'MAXIMA', output results

printf "problem: %s\n", s/\n/ /gr; # condensed problem statement

my $maxima_vars = join("\$\n", uniq @vars);
my $maxima_eqns = '['. join(', ', @eqns) . ']';
my $maxima_find = '['. join(', ', map {"n_$_"} @types) . ']';

if (@eqns and @vars) {
my ($fh, $maxima_script) = tempfile(UNLINK => 1);
open $fh, '>', $maxima_script or die "Couldn't open temporary file: $!\n";
print $fh <<~"END";
$maxima_vars\$
solve($maxima_eqns, $maxima_find);
END
close $fh;

open my $maxima_output, "/opt/local/bin/maxima -q -b $maxima_script |" or die "Couldn't open maxima: $!\n";
while (<$maxima_output>) {
print "solution: $1\n" if /\(\%o\d+\)\s+\[\[([^\]]+)\]\]/; # only display solution
}
close $maxima_output;
} else {
print "Couldn't deduce enough information to formulate equations.\n"
}
}
close MAXIMA;
print "\n";
unlink $temp;
} else {
print "Couldn't deduce enough information to formulate equations.\n"
}
print "\n\n";
}
}

</lang>
__DATA__
The following is an example '''input''' file:
<pre>
# Bluman, Allan G. Math word problems demystified. 2005. The McGraw-Hill Companies Inc. p. 112, problem 1
If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.
If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.


# Ibid., p. 112, problem 2
A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.
A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.


# Ibid., p. 112, problem 3
A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.
A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.


A childs bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.
# Ibid., p. 112, problem 4
A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.


# Ibid., p. 112, problem 5
A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.


# Ibid., p. 112, problem 6
In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.
In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.


# Ibid., p. 112, problem 7
A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.

# Ibid., p. 112, problem 8
A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.

# Ibid., p. 112, problem 9
An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?

# Ibid., p. 112, problem 10
A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?
A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?


# Ibid., p. 109
A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?
A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?


# Ibid., p. 110
A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?
A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?


# Ibid., p. 111
A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.

# Ibid., p. 119, problem 8
A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.
A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.


# Ibid., p. 120, problem 9
A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.
A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.


# Ibid., p. 120, problem 10
A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.


The twenty-six coins in my pocket are all dollar coins and quarters, and they add up to seventeen dollars in value. How many of each coin are there?
# More test problems from around the web...


# Source: http://www.purplemath.com/modules/coinprob.htm
# Soln: 12 quarters, 14 dollar coins
Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?

# Ibid.
# Soln: Then there are six quarters, and I can work backwards to figure out that there are 9 dimes and 18 nickels.
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?


# Ibid.
# Soln. There are nine of each type of coin in the wallet.
A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?


# Source: http://www.algebralab.org/Word/Word.aspx?file=Algebra_CoinProblems.xml
# Soln: Ken has 17 nickels and 8 dimes.
Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?


# Ibid.
# Let's Practice
# Question #1
# Note: The original question had an inconsistency in it,
# namely "Terry has 7 more" should be "Terry has 2 more..."
# Soln: Terry has 18 dimes and 20 quarters.
Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?


# Ibid.
# Question #2
# Soln: There are 2 ten-dollar bills, 8 one-dollar bills, and 3 five-dollar bills.
In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?
In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?


# Ibid.
# Try These
# Question #1
Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?
Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?


# Ibid.
# Question #2
A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine.
A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine.


# Source: http://voices.yahoo.com/how-set-solve-coin-word-problems-algebra-1713709.html

# Sample Coin Word Problem 1:
# Soln: Michael has 15 dimes and 12 quarters.
Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?
Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?


# Ibid.
# Sample Coin Word Problem 2:
# Soln: Lucille has 25 quarters and 140 nickels.
Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?
Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?


# Ibid.
# Sample Coin Word Problem 3:
# Soln: Ben has 150 dimes and 121 quarters.
Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?
Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?


A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?</syntaxhighlight>
# Source: http://www.calculatorsoup.com/calculators/wordproblems/algebrawordproblem1.php
{{out}}
A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
<pre>problem: person 3 times as many quarter as dime and total amount money $ 5.95 , find number quarter and dime .
</pre>
And this is the resulting '''output''' file. Each section contains a citation of the source of the input, the original input, the MAXIMA script as formulated by the perl script, and the solution extracted from the MAXIMA output:
<pre>
# Bluman, Allan G. Math word problems demystified. 2005. The McGraw-Hill Companies Inc. p. 112, problem 1
original input: If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.
v_quarter: 25$
v_dime: 10$
total: 595$
solve([n_quarter = 3 * n_dime, total = n_quarter * v_quarter + n_dime * v_dime], [n_quarter, n_dime]);
solution: n_quarter = 21, n_dime = 7
solution: n_quarter = 21, n_dime = 7


problem: pile 18 coin consists penny and nickel . total amount coin 38 ¢ , find number penny and nickel .
# Ibid., p. 112, problem 2
original input: A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.
v_nickel: 5$
v_penny: 1$
count: 18$
total: 38$
solve([total = n_nickel * v_nickel + n_penny * v_penny, count = n_nickel + n_penny], [n_nickel, n_penny]);
solution: n_nickel = 5, n_penny = 13
solution: n_nickel = 5, n_penny = 13


problem: small child 6 more quarter than nickel . total amount coin $ 3.0 , find number nickel and quarter child .
# Ibid., p. 112, problem 3
original input: A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.
v_quarter: 25$
v_nickel: 5$
total: 300$
solve([n_quarter = n_nickel + 6, total = n_quarter * v_quarter + n_nickel * v_nickel], [n_quarter, n_nickel]);
solution: n_quarter = 11, n_nickel = 5
solution: n_quarter = 11, n_nickel = 5


problem: childs bank contains 32 coin consisting nickel and quarter . total amount money $ 3.80 , find number nickel and quarter in bank .
# Ibid., p. 112, problem 4

original input: A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.
v_quarter: 25$
v_nickel: 5$
count: 32$
total: 380$
solve([total = n_quarter * v_quarter + n_nickel * v_nickel, count = n_quarter + n_nickel], [n_quarter, n_nickel]);
solution: n_quarter = 11, n_nickel = 21
solution: n_quarter = 11, n_nickel = 21


problem: person 2 times as many dime as penny and 3 more nickel than penny . total amount coin $ 1.97 , find numbers each type coin person .
# Ibid., p. 112, problem 5
original input: A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
v_dime: 10$
v_nickel: 5$
v_penny: 1$
total: 197$
solve([n_dime = 2 * n_penny, n_nickel = n_penny + 3, total = n_dime * v_dime + n_nickel * v_nickel + n_penny * v_penny], [n_dime, n_nickel, n_penny]);
solution: n_dime = 14, n_nickel = 10, n_penny = 7
solution: n_dime = 14, n_nickel = 10, n_penny = 7


problem: in bank , 3 times as many quarter as half_dollar and 6 more dime than half_dollar . total amount money in bank $ 4.65 , find number each type coin in bank .
# Ibid., p. 112, problem 6
original input: In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.
v_half_dollar: 50$
v_quarter: 25$
v_dime: 10$
total: 465$
solve([n_quarter = 3 * n_half_dollar, n_dime = n_half_dollar + 6, total = n_half_dollar * v_half_dollar + n_quarter * v_quarter + n_dime * v_dime], [n_half_dollar, n_quarter, n_dime]);
solution: n_half_dollar = 3, n_quarter = 9, n_dime = 9
solution: n_half_dollar = 3, n_quarter = 9, n_dime = 9


problem: clerk given $ 75 in bill put in cash drawer start workday . 2 times as many $ 1 bill as $ 5 bill and 1 less $ 10 bill than $ 5 bill . how many each type bill ?
# Ibid., p. 112, problem 7
original input: A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.
count: 12$
v_37_stamp: 37$
v_23_stamp: 23$
total: 374$
solve([total = n_37_stamp * v_37_stamp + n_23_stamp * v_23_stamp, count = n_37_stamp + n_23_stamp], [n_37_stamp, n_23_stamp]);
solution: n_37_stamp = 7, n_23_stamp = 5

# Ibid., p. 112, problem 8
original input: A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.
count: 80$
v_sandwiches: 69$
v_bars: 75$
total: 5880$
solve([total = n_sandwiches * v_sandwiches + n_bars * v_bars, count = n_sandwiches + n_bars], [n_sandwiches, n_bars]);
solution: n_sandwiches = 20, n_bars = 60

# Ibid., p. 112, problem 9
original input: An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?
v_college_ruled_notebook_paper: 159$
v_wide_ruled_notebook_paper: 229$
count: 9$
total: 1571$
solve([total = n_college_ruled_notebook_paper * v_college_ruled_notebook_paper + n_wide_ruled_notebook_paper * v_wide_ruled_notebook_paper, count = n_college_ruled_notebook_paper + n_wide_ruled_notebook_paper], [n_college_ruled_notebook_paper, n_wide_ruled_notebook_paper]);
solution: n_college_ruled_notebook_paper = 7, n_wide_ruled_notebook_paper = 2

# Ibid., p. 112, problem 10
original input: A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?
total: 7500$
v_1: 100$
v_5: 500$
v_10: 1000$
solve([n_1 = 2 * n_5, n_1 = 2 * n_5, n_10 = n_5 - 1, total = n_1 * v_1 + n_5 * v_5 + n_10 * v_10], [n_1, n_5, n_10, n_5]);
solution: n_1 = 10, n_10 = 4, n_5 = 5
solution: n_1 = 10, n_10 = 4, n_5 = 5


problem: person 8 coin consisting quarter and dime . total amount change $ 1.25 , how many each kind coin ?
# Ibid., p. 109
original input: A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?
v_quarter: 25$
v_dime: 10$
count: 8$
total: 125$
solve([total = n_quarter * v_quarter + n_dime * v_dime, count = n_quarter + n_dime], [n_quarter, n_dime]);
solution: n_quarter = 3, n_dime = 5
solution: n_quarter = 3, n_dime = 5


problem: person 3 times as many dime as nickel and 5 more penny than nickel . total amount these coin $ 1.13 , how many each kind coin ?
# Ibid., p. 110
original input: A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?
v_dime: 10$
v_nickel: 5$
v_penny: 1$
total: 113$
solve([n_dime = 3 * n_nickel, n_penny = n_nickel + 5, total = n_dime * v_dime + n_nickel * v_nickel + n_penny * v_penny], [n_dime, n_nickel, n_penny]);
solution: n_dime = 9, n_nickel = 3, n_penny = 8
solution: n_dime = 9, n_nickel = 3, n_penny = 8


problem: person 9 more dime than nickel . total amount money $ 1.20 , find number dime person .
# Ibid., p. 111
original input: A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.
count: 10$
total: 1700$
v_birthday_cards: 150$
v_anniversary_cards: 200$
solve([total = n_birthday_cards * v_birthday_cards + n_anniversary_cards * v_anniversary_cards, count = n_birthday_cards + n_anniversary_cards], [n_birthday_cards, n_anniversary_cards]);
solution: n_birthday_cards = 6, n_anniversary_cards = 4

# Ibid., p. 119, problem 8
original input: A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.
v_dime: 10$
v_nickel: 5$
total: 120$
solve([n_dime = n_nickel + 9, total = n_dime * v_dime + n_nickel * v_nickel], [n_dime, n_nickel]);
solution: n_dime = 11, n_nickel = 2
solution: n_dime = 11, n_nickel = 2


problem: person 20 bill consisting $ 1 bill and $ 2 bill . total amount money person $ 35 , find number $ 2 bill person .
# Ibid., p. 120, problem 9
original input: A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.
count: 20$
total: 3500$
v_1: 100$
v_2: 200$
solve([total = n_1 * v_1 + n_2 * v_2, count = n_1 + n_2], [n_1, n_2, n_2]);
solution: n_1 = 5, n_2 = 15
solution: n_1 = 5, n_2 = 15


problem: bank contains 8 more penny than nickel and 3 more dime than nickel . total amount money in bank $ 3.10 , find number dime in bank .
# Ibid., p. 120, problem 10
original input: A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
v_dime: 10$
v_nickel: 5$
v_penny: 1$
total: 310$
solve([n_penny = n_nickel + 8, n_dime = n_nickel + 3, total = n_dime * v_dime + n_nickel * v_nickel + n_penny * v_penny], [n_dime, n_nickel, n_penny]);
solution: n_dime = 20, n_nickel = 17, n_penny = 25
solution: n_dime = 20, n_nickel = 17, n_penny = 25


problem: 26 coin in my pocket all dollar_coin and quarter , and add up $ 17 in value . how many each coin ?
# More test problems from around the web...
# Source: http://www.purplemath.com/modules/coinprob.htm
# Soln: 12 quarters, 14 dollar coins
original input: Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
v_dollar_coin: 100$
v_quarter: 25$
count: 26$
total: 1700$
solve([total = n_dollar_coin * v_dollar_coin + n_quarter * v_quarter, count = n_dollar_coin + n_quarter], [n_dollar_coin, n_quarter]);
solution: n_dollar_coin = 14, n_quarter = 12
solution: n_dollar_coin = 14, n_quarter = 12


problem: collection 33 coin , consisting nickel , dime , and quarter , value $ 3.30 . 3 times as many nickel as quarter , and 0.5 as many dime as nickel , how many coin each kind ?
# Ibid.
# Soln: Then there are six quarters, and I can work backwards to figure out that there are 9 dimes and 18 nickels.
original input: A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
v_quarter: 25$
v_dime: 10$
v_nickel: 5$
count: 33$
total: 330$
solve([n_nickel = 3 * n_quarter, n_dime = 0.5 * n_nickel, total = n_quarter * v_quarter + n_dime * v_dime + n_nickel * v_nickel, count = n_quarter + n_dime + n_nickel], [n_quarter, n_dime, n_nickel]);
solution: n_quarter = 6, n_dime = 9, n_nickel = 18
solution: n_quarter = 6, n_dime = 9, n_nickel = 18


problem: wallet contains same number penny , nickel , and dime . coin total $ 1.44 . how many each type coin wallet contain ?
# Ibid.
# Soln. There are nine of each type of coin in the wallet.
original input: A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
v_dime: 10$
v_nickel: 5$
v_penny: 1$
total: 144$
solve([n_penny = n_nickel, n_nickel = n_dime, total = n_dime * v_dime + n_nickel * v_nickel + n_penny * v_penny], [n_dime, n_nickel, n_penny]);
solution: n_dime = 9, n_nickel = 9, n_penny = 9
solution: n_dime = 9, n_nickel = 9, n_penny = 9


problem: suppose ken 25 coin in nickel and dime only and total $ 1.65 . how many each coin ?
# Source: http://www.algebralab.org/Word/Word.aspx?file=Algebra_CoinProblems.xml
# Soln: Ken has 17 nickels and 8 dimes.
original input: Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
v_dime: 10$
v_nickel: 5$
count: 25$
total: 165$
solve([total = n_dime * v_dime + n_nickel * v_nickel, count = n_dime + n_nickel], [n_dime, n_nickel]);
solution: n_dime = 8, n_nickel = 17
solution: n_dime = 8, n_nickel = 17


problem: terry 2 more quarter than dime and total $ 6.80 . number quarter and dime 38 . how many quarter and dime terry ?
# Ibid.
# Let's Practice
# Question #1
# Note: The original question had an inconsistency in it,
# namely "Terry has 7 more" should be "Terry has 2 more..."
# Soln: Terry has 18 dimes and 20 quarters.
original input: Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
v_quarter: 25$
v_dime: 10$
count: 38$
total: 680$
solve([n_quarter = n_dime + 2, total = n_quarter * v_quarter + n_dime * v_dime, count = n_quarter + n_dime], [n_quarter, n_dime]);
solution: n_quarter = 20, n_dime = 18
solution: n_quarter = 20, n_dime = 18


problem: in my wallet , $ 1 bill , $ 5 bill , and $ 10 bill . total amount in my wallet $ 43 . 4 times as many $ 1 bill as $ 10 bill . all together , 13 bill in my wallet . how many each bill ?
# Ibid.
# Question #2
# Soln: There are 2 ten-dollar bills, 8 one-dollar bills, and 3 five-dollar bills.
original input: In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?
count: 13$
total: 4300$
v_1: 100$
v_5: 500$
v_10: 1000$
solve([n_1 = 4 * n_10, n_1 = 4 * n_10, total = n_1 * v_1 + n_5 * v_5 + n_10 * v_10, count = n_1 + n_5 + n_10], [n_1, n_5, n_10, n_1, n_10]);
solution: n_5 = 3, n_1 = 8, n_10 = 2
solution: n_5 = 3, n_1 = 8, n_10 = 2


problem: marsha 3 times as many $ 1 bill as $ 5 bill . total $ 32 . how many each bill ?
# Ibid.
# Try These
# Question #1
original input: Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?
total: 3200$
v_1: 100$
v_5: 500$
solve([n_1 = 3 * n_5, n_1 = 3 * n_5, total = n_1 * v_1 + n_5 * v_5], [n_1, n_5]);
solution: n_1 = 12, n_5 = 4
solution: n_1 = 12, n_5 = 4


problem: vending machine $ 41.25 in . 255 coin total and machine only accepts nickel , dime and quarter . 2 times as many dime as nickel . how many each coin in machine .
# Ibid.
# Question #2
original input: A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine.
v_quarter: 25$
v_dime: 10$
v_nickel: 5$
count: 255$
total: 4125$
solve([n_dime = 2 * n_nickel, total = n_quarter * v_quarter + n_dime * v_dime + n_nickel * v_nickel, count = n_quarter + n_dime + n_nickel], [n_quarter, n_dime, n_nickel]);
solution: n_quarter = 120, n_dime = 90, n_nickel = 45
solution: n_quarter = 120, n_dime = 90, n_nickel = 45


problem: michael had 27 coin in all , valuing $ 4.50 . had only quarter and dime , how many coin each kind ?
# Source: http://voices.yahoo.com/how-set-solve-coin-word-problems-algebra-1713709.html
# Sample Coin Word Problem 1:
# Soln: Michael has 15 dimes and 12 quarters.
original input: Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?
v_quarter: 25$
v_dime: 10$
count: 27$
total: 450$
solve([total = n_quarter * v_quarter + n_dime * v_dime, count = n_quarter + n_dime], [n_quarter, n_dime]);
solution: n_quarter = 12, n_dime = 15
solution: n_quarter = 12, n_dime = 15


problem: lucille had $ 13.25 in nickel and quarter . had 165 coin in all , how many each type coin ?
# Ibid.
# Sample Coin Word Problem 2:
# Soln: Lucille has 25 quarters and 140 nickels.
original input: Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?
v_quarter: 25$
v_nickel: 5$
count: 165$
total: 1325$
solve([total = n_quarter * v_quarter + n_nickel * v_nickel, count = n_quarter + n_nickel], [n_quarter, n_nickel]);
solution: n_quarter = 25, n_nickel = 140
solution: n_quarter = 25, n_nickel = 140


problem: ben $ 45.25 in quarter and dime . 29 less quarter than dime , how many each type coin ?
# Ibid.
# Sample Coin Word Problem 3:
# Soln: Ben has 150 dimes and 121 quarters.
original input: Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?
v_quarter: 25$
v_dime: 10$
total: 4525$
solve([n_quarter = n_dime - 29, total = n_quarter * v_quarter + n_dime * v_dime], [n_quarter, n_dime]);
solution: n_quarter = 121, n_dime = 150
solution: n_quarter = 121, n_dime = 150


problem: person 12 coin consisting dime and penny . total amount money $ 0.30 , how many each coin ?
# Source: http://www.calculatorsoup.com/calculators/wordproblems/algebrawordproblem1.php
solution: n_dime = 2, n_penny = 10</pre>
original input: A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?

v_dime: 10$
=={{header|Phix}}==
v_penny: 1$
The title of this task is solving <i>coin</i> problems, therefore I have ruthlessly eradicated stamps, sandwiches, paper, and cards.
count: 12$
It just adds unnecessary fiddling, along with the need to add custom assets and asset-values, such as 37c stamps, $1.50 cards, etc.
total: 30$
Hence this covers 24/28 of the Perl/Go examples. On the plus side, there is no hard limit on the number of unknowns,
solve([total = n_dime * v_dime + n_penny * v_penny, count = n_dime + n_penny], [n_dime, n_penny]);
though all examples below are for 2 and 3 only. A couple (14 and 17) also sail perilously close to getting a divide by zero.
solution: n_dime = 2, n_penny = 10
This task was quite a bit of fun, once I got stuck in.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #000080;font-style:italic;">-- demo\rosetta\Solving_coin_problems.exw</span>
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">source</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"""
If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.
--==&gt;expected:quarters = 21, dimes = 7
A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38c, find the number of pennies and nickels.
--==&gt;expected:pennies = 13, nickels = 5
A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.
--==&gt;expected:quarters = 11, nickels = 5
A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.
--==&gt;expected:nickels = 21, quarters = 11
A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
--==&gt;expected:dimes = 14, pennies = 7, nickels = 10
In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.
--==&gt;expected:quarters = 9, half_dollars = 3, dimes = 9
A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?
--==&gt;expected:one_dollar_bills = 10, five_dollar_bills = 5, ten_dollar_bills = 4
A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?
--==&gt;expected:quarters = 3, dimes = 5
A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?
--==&gt;expected:dimes = 9, nickels = 3, pennies = 8
A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.
--==&gt;expected:dimes = 11, nickels = 2
A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.
--==&gt;expected:one_dollar_bills = 5, two_dollar_bills = 15
A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
--==&gt;expected:pennies = 25, nickels = 17, dimes = 20
Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
--==&gt;expected:dollars = 14, quarters = 12
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
--==&gt;expected:nickels = 18, dimes = 9, quarters = 6
A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
--==&gt;expected:pennies = 9, nickels = 9, dimes = 9
Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
--==&gt;expected:nickels = 17, dimes = 8
Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
--==&gt;expected:quarters = 20, dimes = 18
In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?
--==&gt;expected:one_dollar_bills = 8, five_dollar_bills = 3, ten_dollar_bills = 2
Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?
--==&gt;expected:one_dollar_bills = 12, five_dollar_bills = 4
A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine.
--==&gt;expected:nickels = 45, dimes = 90, quarters = 120
Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?
--==&gt;expected:quarters = 12, dimes = 15
Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?
--==&gt;expected:nickels = 140, quarters = 25
Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?
--==&gt;expected:quarters = 121, dimes = 150
A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
--==&gt;expected:dimes = 2, pennies = 10"""</span><span style="color: #0000FF;">,</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">texts</span><span style="color: #0000FF;">,</span><span style="color: #000000;">replacements</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">({{</span><span style="color: #008000;">"."</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" ."</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">","</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" ,"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"had"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"has"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"contain?"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"have?"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"there?"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"have?"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"has ."</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"have?"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"in the bank ."</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"have?"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"in the machine ."</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"have?"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"as many"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"asmany"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">" , and they add up"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" . total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">" , has a value"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" . total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">" only and has a total"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" . total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">" and has a total"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" . total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"All together ,"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"A vending machine has"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"valuing"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"coins in all ,"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"coins ."</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"coins total and"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"coins ."</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"find"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"many"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"consists"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"consisting"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"twenty-six"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"26"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"seventeen dollars in value"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"$17.00"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">" one "</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" 1 "</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"three"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"3"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"four"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"4"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"twice"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"2 times"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"ten"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"10"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">" and the total"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" . total"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"half dollars"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"half_dollars"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"$1 bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"one_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"$2 bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"two_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"$5 bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"five_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"$10 bill"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"ten_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"one-dollar bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"one_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"five-dollar bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"five_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"five dollar bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"five_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"10-dollar bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"ten_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"10_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"ten_dollar_bills"</span><span style="color: #0000FF;">}}),</span>
<span style="color: #000000;">noise</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"the|a|to|of|i|is|that|it|on|you|this|for|but|with|are|have|be|at|or|was|so|if|out|not|he|she|they|has|do|does"</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"|in|these|person|small|child|child's|bank|pile|clerk|given|put|there|cash|drawer|start|workday|his|suppose|ken"</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"|terry|how|my|marsha|machine|accepts|michael|lucille|ben|number|type|kind|amount|collection|contains|change"</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"|wallet|did|numbers|pocket"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"|"</span><span style="color: #0000FF;">),</span>
<span style="color: #000080;font-style:italic;">-- one spectacularly irksome preamble containing absolutely no useful information whatsoever...:</span>
<span style="color: #000000;">uncle</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"your uncle walks in , jingling the coins in his pocket . "</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"he grins at you and tells you that you can have all the coins "</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"if you can figure out how many of each kind of coin he is carrying . "</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"you're not too interested until he tells you that he's been collecting "</span><span style="color: #0000FF;">&</span>
<span style="color: #008000;">"those gold-tone one-dollar coins . "</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">vocab</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #008000;">"times"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"asmany"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"quarters"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"as"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"dimes"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"and"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"total"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"money"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"many"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"have?"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"coins"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"consisting"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"pennies"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"nickels"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"more"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"less"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"than"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"each"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"coin"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"half_dollars"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"bill"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"all"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"dollars"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"one-half"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"same"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"only"</span><span style="color: #0000FF;">,</span>
<span style="color: #008000;">"one_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"two_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"five_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"ten_dollar_bills"</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">assets</span><span style="color: #0000FF;">,</span><span style="color: #000000;">assetv</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">columnize</span><span style="color: #0000FF;">({{</span><span style="color: #008000;">"ten_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"five_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">500</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"two_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">200</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"one_dollar_bills"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"dollars"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">100</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"half_dollars"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"quarters"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"dimes"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"nickels"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #008000;">"pennies"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}})</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">count</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">lines</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">substitute_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">source</span><span style="color: #0000FF;">,</span><span style="color: #000000;">texts</span><span style="color: #0000FF;">,</span><span style="color: #000000;">replacements</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">expectations</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">vused</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vocab</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">cleanup_lines</span><span style="color: #0000FF;">()</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">words</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">by</span> <span style="color: #000000;">2</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">li</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">lower</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"your uncle"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">li</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- note: if you tweak texts/replacements then you may
-- need to tweak the uncle constant to match.</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #000000;">uncle</span><span style="color: #0000FF;">,</span><span style="color: #000000;">li</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">li</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">li</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">uncle</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">li</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">noise</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">remove_all</span><span style="color: #0000FF;">(</span><span style="color: #000000;">noise</span><span style="color: #0000FF;">[</span><span style="color: #000000;">n</span><span style="color: #0000FF;">],</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[$]=</span><span style="color: #008000;">"."</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],{</span><span style="color: #008000;">"dimes"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"nickels"</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">words</span><span style="color: #0000FF;">[$]</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">"have?"</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">","</span> <span style="color: #008080;">then</span> <span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">2</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">-- re-join eg "$3" and ".99" (oops)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">])></span><span style="color: #000000;">1</span> <span style="color: #008080;">and</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">'.'</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">w</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]&</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">]}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">({</span><span style="color: #008000;">","</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"many"</span><span style="color: #0000FF;">},</span><span style="color: #000000;">words</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"."</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"many"</span><span style="color: #0000FF;">})</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">match_replace</span><span style="color: #0000FF;">({</span><span style="color: #008000;">","</span><span style="color: #0000FF;">},</span><span style="color: #000000;">words</span><span style="color: #0000FF;">,{})</span>
<span style="color: #000000;">count</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">count</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span>
<span style="color: #000000;">li</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">match</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"--==&gt;expected:"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">li</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">li</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">li</span><span style="color: #0000FF;">[</span><span style="color: #000000;">15</span><span style="color: #0000FF;">..$]</span>
<span style="color: #000000;">li</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">substitute</span><span style="color: #0000FF;">(</span><span style="color: #000000;">li</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" ,"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">","</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">expectations</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">expectations</span><span style="color: #0000FF;">,</span><span style="color: #000000;">li</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">lines</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">count</span><span style="color: #0000FF;">]</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d puzzles:\n"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">count</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Step 1: remove noise and otherwise simplify (if nothing else, down to a %d-word vocab):\n\n"</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">vocab</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">count</span> <span style="color: #008080;">do</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #000000;">cleanup_lines</span><span style="color: #0000FF;">()</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">word</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">word</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">and</span> <span style="color: #008080;">not</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">word</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"as"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"consisting"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"all"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"and"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"than"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"only"</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span><span style="color: #000000;">word</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">unknowns</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">parse_sentence</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">-- Converts eg {"$1.00","quarters","and","nickels"} to {100,25,5}.
-- An "equation" of {100,25,5} means "100==25*unknown[1]+5*unknown[2]".
-- Obviously this is suitably scruffy, but the 31-word vocab certainly helps!
-- It is worth noting that by this stage most sentences begin or end in a number.
-- Since we may not have the full set of unknowns, each equation ends with a code:
-- 0: pad with 0, 1: pad with 1, 'a': pad with the unknown asset values</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">rest</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">isnumber</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">set_asset_sum</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">false</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">ww</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ww</span><span style="color: #0000FF;">,</span><span style="color: #000000;">vocab</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">r</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">scanf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ww</span><span style="color: #0000FF;">,{</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%dc"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"$%f"</span><span style="color: #0000FF;">}[</span><span style="color: #000000;">f</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">!={}</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iif</span><span style="color: #0000FF;">(</span><span style="color: #000000;">f</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span><span style="color: #0000FF;">?</span><span style="color: #7060A8;">round</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]*</span><span style="color: #000000;">100</span><span style="color: #0000FF;">):</span><span style="color: #000000;">r</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">={}</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">ww</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">vused</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"times"</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"asmany"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"and"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">rest</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$]</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- eg {"3","times","asmany","quarters","as","dimes"}</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">6</span> <span style="color: #008080;">or</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"as"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">..</span><span style="color: #000000;">6</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">6</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"coins"</span>
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"bills"</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)></span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">--/* eg:
{"18","coins","consisting","pennies","and","nickels"}
{"26","coins","all","dollars","and","quarters"}
{"25","coins","nickels","and","dimes"}
{"33","coins","consisting","nickels","dimes","and","quarters"}
{"27","coins"}
{"20","bills","consisting","one_dollar_bills","and","two_dollar_bills"}
--*/</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">..$])</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]}&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],{</span><span style="color: #008000;">"more"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"less"</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"and"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">rest</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$]</span>
<span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">--/* eg:
{"5","more","pennies","than","nickels"}
{"29","less","quarters","than","dimes"}
--*/</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">5</span> <span style="color: #008080;">or</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"than"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">..$])</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]}&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">))</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">less</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"less"</span><span style="color: #0000FF;">?-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">:+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">less</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">less</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000080;font-style:italic;">--/* eg:
{"$75","bills"}
{"$45.25","quarters","and","dimes"}
--*/</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)></span><span style="color: #000000;">2</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- log assets:
-- eg {"$13.25","nickels","and","quarters"}</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"and"</span> <span style="color: #008080;">or</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">4</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]}</span>
<span style="color: #000000;">set_asset_sum</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[$]</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"total"</span>
<span style="color: #008080;">or</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">3</span> <span style="color: #008080;">and</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]={</span><span style="color: #008000;">"coins"</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"total"</span><span style="color: #0000FF;">})</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">--/*
{"total","money","$5.95"}
{"total","coins","38c"}
{"total","coins","$3.00"}
{"total","$3.74"}
{"total","cost","$17.00"}
{"coins","total","$1.44"}
--*/</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[$]}</span>
<span style="color: #000000;">set_asset_sum</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">else</span>
<span style="color: #000080;font-style:italic;">-- eg {"quarters","and","dimes","38"}</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[$]}&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"one-half"</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- eg {"one-half","asmany","dimes","as","nickels"}</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">5</span> <span style="color: #008080;">or</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"asmany"</span> <span style="color: #008080;">or</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"as"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">..$])</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">2</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">5</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"many"</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">--/* eg
{"many","quarters","and","dimes","have?"}
{"many","each","coin","have?"}
{"many","each","have?"}
{"many","each","bill","have?"}
{"many","dimes","have?"}
{"many","coins","each","have?"}
--*/</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[$]!=</span><span style="color: #008000;">"have?"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000080;font-style:italic;">-- no rule, as yet, just outputs everything instead.</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"same"</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- eg {"same","pennies","nickels","and","dimes"}</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$])</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">3</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- (p==n)</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">})</span> <span style="color: #000080;font-style:italic;">-- (n==d)</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]=</span><span style="color: #008000;">"total"</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- eg {"total","13","bills"}</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">3</span> <span style="color: #008080;">or</span> <span style="color: #008080;">not</span> <span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">or</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">3</span><span style="color: #0000FF;">]!=</span><span style="color: #008000;">"bills"</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">isnumber</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]}&</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">))</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">1</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">else</span>
<span style="color: #000080;font-style:italic;">--/* eg:
{"one_dollar_bills","five_dollar_bills","and","ten_dollar_bills"}
{"only","nickels","dimes","and","quarters"}
{"only","quarters","and","dimes"}
--*/
-- just log assets:</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">add_unknowns</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">words</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">set_asset_sum</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- common code for eg {"total","$3.74"} and {"$75","bills"}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">u</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">uu</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">unknowns</span><span style="color: #0000FF;">[</span><span style="color: #000000;">u</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">uu</span><span style="color: #0000FF;">,</span><span style="color: #000000;">assets</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">assetv</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">sentence</span> <span style="color: #0000FF;">&=</span> <span style="color: #008000;">'a'</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentence</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rest</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- {sequence s2,unknowns} = parse_sentence(rest,unknowns)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s2</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">s2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">parse_sentence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">s2</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">solveN</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">string</span> <span style="color: #000000;">expected</span><span style="color: #0000FF;">)</span>
<span style="color: #000080;font-style:italic;">--
-- Based on https://mathcs.clarku.edu/~djoyce/ma105/simultaneous.html
-- aka the ancient Chinese Jiuzhang suanshu ~100 B.C. (!!)
--
-- Example (ignoring n, which is solely for output):
-- rules = {{18,1,1},{38,1,5}}, ie 18==p+n, 38==p+5*n
-- unknowns = {"pennies","nickels"}
-- expected = "pennies = 13, nickels = 5"
--
-- In the elimination phase, both p have multipliers of 1, so we can
-- ignore those two sq_mul and just do (38=p+5n)-(18=p+n)==&gt;(20=4n).
-- Obviously therefore n is 5 and substituting backwards p is 13.
--</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">res</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">ri</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rj</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">rii</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rji</span>
<span style="color: #000000;">rules</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">-- successively eliminate (grow lower left triangle of 0s)</span>
<span style="color: #000000;">ri</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ri</span><span style="color: #0000FF;">)!=</span><span style="color: #000000;">l</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">rii</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rii</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">rj</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">rji</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rji</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">rj</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rj</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rii</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ri</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rji</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- (job done)</span>
<span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">l</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">-- then substitute each backwards</span>
<span style="color: #000000;">ri</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">rii</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]/</span><span style="color: #000000;">ri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #000080;font-style:italic;">-- (all else should be 0)</span>
<span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%s = %d"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],</span><span style="color: #000000;">rii</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">rj</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">rji</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">rji</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">rji</span><span style="color: #0000FF;">*</span><span style="color: #000000;">rii</span>
<span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">,</span><span style="color: #008000;">", "</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d: %v ==&gt; %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">res</span><span style="color: #0000FF;">})</span>
<span style="color: #000080;font-style:italic;">-- printf(1,"%d: %s\n",{n,res}) -- (maybe pref.)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">expected</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nStep 2: convert sentences into structures/equations, and solve them:\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">count</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">words</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lines</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">],{</span><span style="color: #008000;">"."</span><span style="color: #0000FF;">})</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{},</span>
<span style="color: #000000;">sentencii</span><span style="color: #0000FF;">,</span> <span style="color: #000080;font-style:italic;">-- (one ...but some still contain "and")</span>
<span style="color: #000000;">unknowns</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">w</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">sentencii</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">parse_sentence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">words</span><span style="color: #0000FF;">[</span><span style="color: #000000;">w</span><span style="color: #0000FF;">],</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">sentencii</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">)></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- messy: puzzle has too much info!
-- (14 aka "33 coins" and 17 "Terry" with 38 coins,
-- eliminate wrongly and get a divide by zero...)
-- sentences = sentences[1..length(unknowns)]</span>
<span style="color: #000000;">sentences</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sentences</span><span style="color: #0000FF;">[-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">sentences</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sentences</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">)!=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000080;font-style:italic;">-- pad any short equations, eg 3 more nickels than dimes
-- needs a 0 for quarters, if were not mentioned before.</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">ss</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sentences</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">padcode</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ss</span><span style="color: #0000FF;">[$]</span>
<span style="color: #000000;">ss</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ss</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..$-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">shortlen</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ss</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">shortlen</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">switch</span> <span style="color: #000000;">padcode</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">ss</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shortlen</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">:</span> <span style="color: #000000;">ss</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shortlen</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">case</span> <span style="color: #008000;">'a'</span><span style="color: #0000FF;">:</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">u</span><span style="color: #0000FF;">=-</span><span style="color: #000000;">shortlen</span> <span style="color: #008080;">to</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">uu</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">unknowns</span><span style="color: #0000FF;">[</span><span style="color: #000000;">u</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #000000;">uu</span><span style="color: #0000FF;">,</span><span style="color: #000000;">assets</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">ss</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">assetv</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">default</span><span style="color: #0000FF;">:</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">switch</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">sentences</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ss</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #000000;">solveN</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">sentences</span><span style="color: #0000FF;">,</span><span style="color: #000000;">unknowns</span><span style="color: #0000FF;">,</span><span style="color: #000000;">expectations</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">k</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">find</span><span style="color: #0000FF;">(</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #000000;">vused</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">k</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?{</span><span style="color: #008000;">"unused vocab"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">vocab</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<!--</syntaxhighlight>-->
{{out}}
You just gotta love this Pidgin English! The problem numbering system used below is mine alone.<br>
I was slightly unsure whether to interpolate these q&a outputs, but I think the separation chosen has its own merits.<br>
The structures/equations of part 2 are completely unreadable at first, but quite simple really.
<pre>
24 puzzles:
Step 1: remove noise and otherwise simplify (if nothing else, down to a 31-word vocab):

1: 3 times asmany quarters as dimes . total money $5.95 . many quarters and dimes have?
2: 18 coins consisting pennies and nickels . total coins 38c . many pennies and nickels have?
3: 6 more quarters than nickels . total coins $3.00 . many nickels and quarters have?
4: 32 coins consisting nickels and quarters . total money $3.80 . many nickels and quarters have?
5: 2 times asmany dimes as pennies and 3 more nickels than pennies . total coins $1.97 . many each coin have?
6: 3 times asmany quarters as half_dollars and 6 more dimes than half_dollars . total money $4.65 . many each coin have?
7: $75 bills . 2 times asmany one_dollar_bills as five_dollar_bills and 1 less ten_dollar_bills than five_dollar_bills . many each bill have?
8: 8 coins consisting quarters and dimes . total $1.25 . many each coin have?
9: 3 times asmany dimes as nickels and 5 more pennies than nickels . total coins $1.13 . many each coin have?
10: 9 more dimes than nickels . total money $1.20 . many dimes have?
11: 20 bills consisting one_dollar_bills and two_dollar_bills . total money $35 . many two_dollar_bills have?
12: 8 more pennies than nickels and 3 more dimes than nickels . total money $3.10 . many dimes have?
13: 26 coins all dollars and quarters . total $17.00 . many each coin have?
14: 33 coins consisting nickels dimes and quarters . total $3.30 . 3 times asmany nickels as quarters and one-half asmany dimes as nickels . many coins each have?
15: same pennies nickels and dimes . coins total $1.44 . many each coin have?
16: 25 coins nickels and dimes . total $1.65 . many each coin have?
17: 2 more quarters than dimes . total $6.80 . quarters and dimes 38 . many quarters and dimes have?
18: one_dollar_bills five_dollar_bills and ten_dollar_bills . total $43 . 4 times asmany one_dollar_bills as ten_dollar_bills . total 13 bills . many each bill have?
19: 3 times asmany one_dollar_bills as five_dollar_bills . total $32 . many each bill have?
20: total $41.25 . 255 coins . only nickels dimes and quarters . 2 times asmany dimes as nickels . many each coin have?
21: 27 coins . total $4.50 . only quarters and dimes . many coins each have?
22: $13.25 nickels and quarters . 165 coins . many each coin have?
23: $45.25 quarters and dimes . 29 less quarters than dimes . many each coin have?
24: 12 coins consisting dimes and pennies . total money $0.30 . many each coin have?

Step 2: convert sentences into structures/equations, and solve them:
1: {{0,1,-3},{595,25,10}} ==> quarters = 21, dimes = 7
2: {{18,1,1},{38,1,5}} ==> pennies = 13, nickels = 5
3: {{6,1,-1},{300,25,5}} ==> quarters = 11, nickels = 5
4: {{32,1,1},{380,5,25}} ==> nickels = 21, quarters = 11
5: {{0,1,-2,0},{3,0,-1,1},{197,10,1,5}} ==> dimes = 14, pennies = 7, nickels = 10
6: {{0,1,-3,0},{6,0,-1,1},{465,25,50,10}} ==> quarters = 9, half_dollars = 3, dimes = 9
7: {{7500,100,500,1000},{0,1,-2,0},{1,0,1,-1}} ==> one_dollar_bills = 10, five_dollar_bills = 5, ten_dollar_bills = 4
8: {{8,1,1},{125,25,10}} ==> quarters = 3, dimes = 5
9: {{0,1,-3,0},{5,0,-1,1},{113,10,5,1}} ==> dimes = 9, nickels = 3, pennies = 8
10: {{9,1,-1},{120,10,5}} ==> dimes = 11, nickels = 2
11: {{20,1,1},{3500,100,200}} ==> one_dollar_bills = 5, two_dollar_bills = 15
12: {{8,1,-1,0},{3,0,-1,1},{310,1,5,10}} ==> pennies = 25, nickels = 17, dimes = 20
13: {{26,1,1},{1700,100,25}} ==> dollars = 14, quarters = 12
14: {{33,1,1,1},{330,5,10,25},{0,1,-2,0}} ==> nickels = 18, dimes = 9, quarters = 6
15: {{0,1,-1,0},{0,0,1,-1},{144,1,5,10}} ==> pennies = 9, nickels = 9, dimes = 9
16: {{25,1,1},{165,5,10}} ==> nickels = 17, dimes = 8
17: {{2,1,-1},{38,1,1}} ==> quarters = 20, dimes = 18
18: {{4300,100,500,1000},{0,1,0,-4},{13,1,1,1}} ==> one_dollar_bills = 8, five_dollar_bills = 3, ten_dollar_bills = 2
19: {{0,1,-3},{3200,100,500}} ==> one_dollar_bills = 12, five_dollar_bills = 4
20: {{4125,5,10,25},{255,1,1,1},{0,-2,1,0}} ==> nickels = 45, dimes = 90, quarters = 120
21: {{27,1,1},{450,25,10}} ==> quarters = 12, dimes = 15
22: {{1325,5,25},{165,1,1}} ==> nickels = 140, quarters = 25
23: {{4525,25,10},{29,-1,1}} ==> quarters = 121, dimes = 150
24: {{12,1,1},{30,10,1}} ==> dimes = 2, pennies = 10
</pre>
</pre>

=={{header|Wren}}==
{{trans|Go}}
{{libheader|Wren-dynamic}}
{{libheader|Wren-pattern}}
{{libheader|Wren-str}}
{{libheader|Wren-sort}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="wren">import "./dynamic" for Struct
import "./pattern" for Pattern
import "./str" for Str
import "./sort" for Sort
import "./fmt" for Fmt

var Kind = Struct.create("Kind", ["name", "value", "number"])

// variable1 = constant1 * variable2 + constant2
var Relation = Struct.create("Relation", ["variable1", "variable2", "constant1", "constant2"])

var nums = {
"one-half": "0 times", "one": "1", "two": "2", "three": "3", "four": "4", "five": "5",
"six": "6", "seven": "7", "eight": "8", "nine": "9", "ten": "10", "eleven": "11", "twelve": "12",
"thirteen": "13", "fourteen": "14", "fifteen": "15", "sixteen": "16", "seventeen": "17",
"eighteen": "18", "nineteen": "19", "twenty": "20", "thirty": "30", "forty": "40",
"fifty": "50", "sixty": "60", "seventy": "70", "eighty": "80", "ninety": "90", "hundred": "100"
}

var nums2 = {
"twenty-": "2", "thirty-": "3", "forty-": "4",
"fifty-": "5", "sixty-": "6", "seventy-": "7", "eighty-": "8", "ninety-": "9"
}

var coins = {
"pennies": 0.01, "nickels": 0.05, "dimes": 0.10, "quarters": 0.25, "half-dollars": 0.50,
"one-dollar": 1.00, "two-dollar": 2.00, "five-dollar": 5.00, "ten-dollar": 10.00
}

var bills = {
"$1": "one-dollar", "$2": "two-dollar", "$5": "five-dollar", "$10": "ten-dollar"
}

var rx1 = Pattern.new("[/$+1/f|+1/d¢]")
var rx2 = Pattern.new("[pennies|nickels|dimes|quarters|half-dollar|one-dollar|two-dollar|five-dollar|ten-dollar]")
var rx3 = Pattern.new("/s[+1/d]/s")
var rx4 = Pattern.new("[+1/d] times as many [+1/y] as [~she has |][+1/y]")
var rx5 = Pattern.new("[+1/d] more [+1/y] than [~she has |][+1/y]")
var rx6 = Pattern.new("[+1/d] less [+1/y] than [~she has |][+1/y]")
var rx7 = Pattern.new("[+1/d] dollars")

var spaced = Fn.new { |s| " %(s) " }

// Gets a sorted list of monetary values.
var getValues = Fn.new { |q|
var ss = rx1.findAll(q).map { |m| m.text.trimEnd(".") }.toList
if (ss.count == 0) return []
var res = []
for (s in ss) {
if (s == "") continue
if (s[0] == "$") {
s = s[1..-1]
} else {
s = "." + s[0..-3] // '¢' is 2 bytes
}
var f = Num.fromString(s)
res.add(f)
}
res.sort()
return res
}

// Gets a sorted slice of non-monetary integers.
var getNumbers = Fn.new { |q|
var ns = rx3.findAll(q).map { |m| m.text }.toList
if (ns.count == 0) return null
var res = []
for (n in ns) {
var i = Num.fromString(n)
res.add(i)
}
res.sort()
return res
}

// Gets the 'kinds' for the problem.
var getKinds = Fn.new { |a|
var num = Num.fromString(a[1])
var kinds = [Kind.new(a[2], 0, 0), Kind.new(a[4], 0, 0)]
var areCoins = false
for (i in 0...kinds.count) {
var v = coins[kinds[i].name]
if (v) {
kinds[i].value = v
areCoins = true
}
}
if (!areCoins) return [0, null]
return [num, kinds]
}

// Checks if the problem involves 3 coins and
// also returns their names and the names of the coins which occur most.
var hasThreeCoins = Fn.new { |q|
q = q.replace(".", "").replace(",", "")
var words = q.split(" ")
var coinMap = {}
for (word in words) {
if (coins.containsKey(word)) {
var v = coinMap[word]
if (v) {
coinMap[word] = v + 1
} else {
coinMap[word] = 1
}
}
}
if (coinMap.count != 3) return [null, "", false]
var maxNum = 0
var maxNames = []
var names = []
for (me in coinMap) {
names.add(me.key)
if (me.value > maxNum) {
maxNum = me.value
maxNames = [me.key]
} else if (me.value == maxNum) {
maxNames.add(me.key)
}
}
return [names, maxNames, true]
}

var errorMsg = Fn.new { |p|
System.print(p)
System.print("*** CAN'T SOLVE THIS ONE ***\n")
}

var printAnswers = Fn.new { |p, kinds|
System.print(p)
System.write("ANSWER:")
var i = 0
for (kind in kinds) {
if (i > 0) System.write(",")
System.write(" %(kind.number) %(kind.name)")
i = i + 1
}
System.print("\n")
}

// Processes a problem which involves 3 coins.
var threeCoins = Fn.new { |p, q, names, maxNames|
var relations = []
var am = rx4.findAll(q).map { |m| [m.text] + m.capsText }.toList
for (i in 0...am.count) {
var res = getKinds.call(am[i])
var mult = res[0]
var kinds = res[1]
relations.add(Relation.new(kinds[0].name, kinds[1].name, mult, 0))
}
var mt = rx5.findAll(q).map { |m| [m.text] + m.capsText }.toList
for (i in 0...mt.count) {
var res = getKinds.call(mt[i])
var plus = res[0]
var kinds = res[1]
relations.add(Relation.new(kinds[0].name, kinds[1].name, 1, plus))
}
var lt = rx6.findAll(q).map { |m| [m.text] + m.capsText }.toList
for (i in 0...lt.count) {
var res = getKinds.call(lt[i])
var minus = res[0]
var kinds = res[1]
relations.add(Relation.new(kinds[0].name, kinds[1].name, 1, -minus))
}
var le = relations.count
if (le > 2) {
errorMsg.call(p)
return
}
if (le == 0) { // numbers of each coin must be the same
var sum = 0
for (name in names) sum = sum + coins[name]
var tv = getValues.call(q)[-1]
var n = (tv/sum + 0.5).floor
var kinds = []
for (name in names) kinds.add(Kind.new(name, 0, n))
printAnswers.call(p, kinds)
} else {
var totalValue = getValues.call(q)[-1]
for (maxName in maxNames) {
for (i in 0...le) {
if (relations[i].constant1 == 0) {
relations[i].constant1 = 0.5 // deals with 'one-half' cases
}
if (le == 2 && maxName == relations[i].variable1) {
var v = relations[i].variable2
relations[i].variable1 = v
relations[i].variable2 = maxName
relations[i].constant1 = 1 / relations[i].constant1
relations[i].constant2 = -relations[i].constant2
}
}
var tv = totalValue
var v1 = ""
var v2 = ""
var v3 = ""
var n1 = 0
var n2 = 0
var n3 = 0
if (le == 2) {
var tmc = coins[relations[0].variable1] * relations[0].constant1 +
coins[relations[1].variable1] * relations[1].constant1 + coins[maxName]
tv = tv - coins[relations[0].variable1] * relations[0].constant2 -
coins[relations[1].variable1] * relations[1].constant2
v1 = maxName
v2 = relations[0].variable1
v3 = relations[1].variable1
n1 = (tv/tmc + 0.5).floor
n2 = (relations[0].constant1*n1 + relations[0].constant2 + 0.5).floor
n3 = (relations[1].constant1*n1 + relations[1].constant2 + 0.5).floor
} else {
var tn = getNumbers.call(q)[-1]
v1 = relations[0].variable1
v2 = relations[0].variable2
for (name in names) {
if (name != v1 && name != v2) {
v3 = name
break
}
}
var mult1 = coins[v1]
var mult2 = coins[v2]
var mult3 = coins[v3]
n2 = (((tn-relations[0].constant2)*mult3-tv+relations[0].constant2*mult1)/
((relations[0].constant1+1)*mult3-relations[0].constant1*mult1-mult2) + 0.5).floor
n1 = (n2*relations[0].constant1 + relations[0].constant2 + 0.5).floor
n3 = tn.floor - n1 - n2
}
var calcValue = n1 * coins[v1] + n2 * coins[v2] + n3 * coins[v3]
if ((totalValue - calcValue).abs <= 1e-14) {
var kinds = [Kind.new(v1, 0, n1), Kind.new(v2, 0, n2), Kind.new(v3, 0, n3)]
printAnswers.call(p, kinds)
return
}
}
errorMsg.call(p)
}
}

var ps = [
"If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.",
"A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.",
"A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.",
"A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.",
"A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.",
"In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.",
"A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.",
"A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.",
"An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?",
"A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?",
"A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?",
"A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?",
"A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.",
"A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.",
"A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.",
"A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.",
"Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?",
"A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?",
"A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?",
"Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?",
"Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?",
"In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?",
"Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?",
"A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?",
"Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?",
"Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?",
"Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?",
"A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?"
]
for (p in ps) {
var q = Str.lower(p).replace("twice", "two times").replace(" does ", " has ")
for (d in ["half", "one", "two", "five", "ten"]) {
q = q.replace(d + " dollar", d + "-dollar")
}
for (me in nums) {
q = q.replace(spaced.call(me.key), spaced.call(me.value))
}
for (me in nums2) {
q = q.replace(me.key, me.value)
}
for (me in nums) {
q = q.replace(me.key + " ", me.value + " ")
}
for (me in bills) {
q = q.replace(me.key + " ", me.value + " ")
}
q = q.replace(" bills", "").replace(" bill", "")
// check if there are 3 coins involved
var res = hasThreeCoins.call(q)
if (res[2]){
threeCoins.call(p, q, res[0], res[1])
continue
}
var am = rx4.findAll(q).map { |m| [m.text] + m.capsText }.toList
if (am.count == 1) {
var res = getKinds.call(am[0])
var mult = res[0]
var kinds = res[1]
if (!kinds) {
errorMsg.call(p)
continue
}
var tv = getValues.call(q)[-1]
kinds[1].number = (tv/(mult*kinds[0].value + kinds[1].value) + 0.5).floor
kinds[0].number = kinds[1].number * mult
printAnswers.call(p, kinds)
continue
}
var mt = rx5.findAll(q).map { |m| [m.text] + m.capsText }.toList
if (mt.count == 1) {
var res = getKinds.call(mt[0])
var plus = res[0]
var kinds = res[1]
if (!kinds) {
errorMsg.call(p)
continue
}
var tv = getValues.call(q)[-1]
kinds[1].number = ((tv-plus*kinds[0].value)/(kinds[0].value + kinds[1].value) + 0.5).floor
kinds[0].number = kinds[1].number + plus
printAnswers.call(p, kinds)
continue
}
var lt = rx6.findAll(q).map { |m| [m.text] + m.capsText }.toList
if (lt.count == 1) {
var res = getKinds.call(lt[0])
var minus = res[0]
var kinds = res[1]
if (!kinds) {
errorMsg.call(p)
continue
}
var tv = getValues.call(q)[-1]
kinds[1].number = ((tv+minus*kinds[0].value)/(kinds[0].value + kinds[1].value) + 0.5).floor
kinds[0].number = kinds[1].number - minus
printAnswers.call(p, kinds)
continue
}
res = getValues.call(q)
var tv = 0
if (res.count > 0) {
tv = res[-1]
} else {
var res3 = rx7.findAll(q).map { |m| [m.text] + m.capsText }.toList
tv = Num.fromString(res3[0][1])
}
var tn = getNumbers.call(q)[-1]
var coinNames = rx2.findAll(q).map { |m| m.text }.toList
Sort.insertion(coinNames)
var kinds = []
if (coinNames.count > 0) {
kinds.add(Kind.new(coinNames[0], coins[coinNames[0]], 0))
for (i in 1...coinNames.count) {
if (coinNames[i] != coinNames[i-1]) {
kinds.add(Kind.new(coinNames[i], coins[coinNames[i]], 0))
}
}
if (kinds.count != 2) {
errorMsg.call(p)
continue
}
} else if (res.count >= 3) {
kinds.add(Kind.new(Fmt.swrite("$$$.2f item", res[0]), res[0], 0))
for (i in 1...res.count-1) {
if (res[i] != res[i-1]) {
kinds.add(Kind.new(Fmt.swrite("$$$.2f item", res[i]), res[i], 0))
}
}
if (kinds.count!= 2) {
errorMsg.call(p)
continue
}
} else {
errorMsg.call(p)
continue
}
kinds[0].number = ((tv-tn*kinds[1].value)/(kinds[0].value-kinds[1].value) + 0.5).floor
kinds[1].number = tn - kinds[0].number
printAnswers.call(p, kinds)
}</syntaxhighlight>

{{out}}
<pre>
If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.
ANSWER: 21 quarters, 7 dimes

A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.
ANSWER: 5 nickels, 13 pennies

A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.
ANSWER: 11 quarters, 5 nickels

A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.
ANSWER: 21 nickels, 11 quarters

A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
ANSWER: 7 pennies, 14 dimes, 10 nickels

In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.
ANSWER: 3 half-dollars, 9 quarters, 9 dimes

A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.
ANSWER: 5 $0.23 item, 7 $0.37 item

A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.
ANSWER: 32 $0.69 item, 48 $0.75 item

An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?
ANSWER: 7 $1.59 item, 2 $2.29 item

A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?
ANSWER: 5 five-dollar, 10 one-dollar, 4 ten-dollar

A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?
ANSWER: 5 dimes, 3 quarters

A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?
ANSWER: 3 nickels, 9 dimes, 8 pennies

A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.
ANSWER: 6 $1.50 item, 4 $2.00 item

A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.
ANSWER: 11 dimes, 2 nickels

A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.
ANSWER: 5 one-dollar, 15 two-dollar

A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
ANSWER: 17 nickels, 25 pennies, 20 dimes

Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
ANSWER: 14 one-dollar, 12 quarters

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
ANSWER: 18 nickels, 6 quarters, 9 dimes

A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
ANSWER: 9 pennies, 9 dimes, 9 nickels

Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
ANSWER: 8 dimes, 17 nickels

Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
ANSWER: 20 quarters, 18 dimes

In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?
ANSWER: 8 one-dollar, 2 ten-dollar, 3 five-dollar

Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?
ANSWER: 12 one-dollar, 4 five-dollar

A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?
ANSWER: 90 dimes, 45 nickels, 120 quarters

Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?
ANSWER: 15 dimes, 12 quarters

Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?
ANSWER: 140 nickels, 25 quarters

Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?
ANSWER: 121 quarters, 150 dimes

A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
ANSWER: 2 dimes, 10 pennies
</pre>

{{omit from|PARI/GP}} <!-- No NLP support and clearly inappropriate for this task -->

Latest revision as of 15:49, 7 February 2024

This task has been flagged for clarification due to it being believed to be too difficult to implement in a reasonable amount of effort in more than one (usually very specialised) language. It may need to be divided into multiple tasks or modified substantially so that multiple implementations are practical, and that may cause code on this page in its current state to be flagged incorrect afterwards. See this page's Talk page for discussion.
Solving coin problems is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

In 1964, Daniel G. Bobrow created the STUDENT AI program in order to solve the types of word problems found in high school algebra books. You can read Bobrow's 1964 Ph.D. thesis, Natural Language Input for a Computer Problem Solving System. The program consists of 3 main pieces:

  1. A pattern matcher that reads the english input,
  2. rules to translate english into equations, and
  3. an algebraic equation solver.

In chapter 7 of his book, Paradigms of Artificial Intelligence Programming: Case Studies in Common Lisp, Peter Norvig lays out the STUDENT program and then challenges his readers as follows:

"Exercise 7.8 [d] Find a mathematically oriented domain that is sufficiently limited so that STUDENT can solve problems in it. The chemistry of solutions (calculating pH concentrations) might be an example. Write the necessary *student-rules*, and test the resulting program." (PAIP, p. 236)

There are several types of word problems commonly encountered in high school algebra, for example coin problems, age problems, distance problems, mixture problems, finance problems, lever problems, and work problems.

For this task, let's focus specifically on coin problems. Example: "If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes." (Bluman, Allan G. Math word problems demystified. 2005. The McGraw-Hill Companies Inc. p. 112, problem 1.)

Coin problems can all pretty much be schematized as follows:

  1. There are types of valuable things:
  2. There are instances of the th type of valuable thing.
  3. The value of the th type of thing is
  4. The total number of things is:
  5. The total value of all the things is:

A typical coin problem wants us to find the , given some of the other information from the schema.

The task is to write an AI program, inspired by Bobrow's STUDENT program and Norvig's challenge in PAIP, capable of solving the kinds of coin problems found in high school algebra.

The program should take coin problems written in plain english and output the solutions. The solutions needn't be output in English.

Go

This relatively simple program can only solve problems with 2 types of coins (or other objects) or 3 types of coins (but not other objects) without the need for an equation solver. However, it is able to solve all 28 problems of these types which were originally listed in the Perl entry before it was restricted to the subset of those problems (24) involving coins and bills. 

package main

import (
    "fmt"
    "math"
    "regexp"
    "sort"
    "strconv"
    "strings"
)

type kind struct {
    name   string
    value  float64
    number int
}

// variable1 = constant1 * variable2 + constant2
type relation struct {
    variable1 string
    variable2 string
    constant1 float64
    constant2 float64
}

var nums = map[string]string{
    "one-half": "0 times", "one": "1", "two": "2", "three": "3", "four": "4", "five": "5",
    "six": "6", "seven": "7", "eight": "8", "nine": "9", "ten": "10", "eleven": "11", "twelve": "12",
    "thirteen": "13", "fourteen": "14", "fifteen": "15", "sixteen": "16", "seventeen": "17",
    "eighteen": "18", "nineteen": "19", "twenty": "20", "thirty": "30", "forty": "40",
    "fifty": "50", "sixty": "60", "seventy": "70", "eighty": "80", "ninety": "90",
    "hundred": "100"}

var nums2 = map[string]string{
    "twenty-": "2", "thirty-": "3", "forty-": "4",
    "fifty-": "5", "sixty-": "6", "seventy-": "7", "eighty-": "8", "ninety-": "9"}

var coins = map[string]float64{
    "pennies": 0.01, "nickels": 0.05, "dimes": 0.10, "quarters": 0.25, "half-dollars": 0.50,
    "one-dollar": 1.00, "two-dollar": 2.00, "five-dollar": 5.00, "ten-dollar": 10.00}

var bills = map[string]string{
    "$1": "one-dollar", "$2": "two-dollar", "$5": "five-dollar", "$10": "ten-dollar"}

var (
    rx1 = regexp.MustCompile(`\$\d+(\.\d+)?|\d+¢`)
    rx2 = regexp.MustCompile(`\b(pennies|nickels|dimes|quarters|half-dollar|one-dollar|two-dollar|five-dollar|ten-dollar)\b`)
    rx3 = regexp.MustCompile(`\s(\d+)\s`)
    rx4 = regexp.MustCompile(`(\d+) times as many ([-\w]+) as (s?he (does|has) )?([-\w]+)`)
    rx5 = regexp.MustCompile(`(\d+) more ([-\w]+) than (s?he (does|has) )?([-\w]+)`)
    rx6 = regexp.MustCompile(`(\d+) less ([-\w]+) than (s?he (does|has) )?([-\w]+)`)
    rx7 = regexp.MustCompile(`(\d+) dollars`)
)

func spaced(s string) string {
    return fmt.Sprintf(" %s ", s)
}

// Gets a sorted slice of monetary values.
func getValues(q string) []float64 {
    ss := rx1.FindAllString(q, -1)
    if ss == nil {
        return nil
    }
    var res []float64
    for _, s := range ss {
        if len(s) == 0 {
            continue
        }
        if s[0] == '$' {
            s = s[1:]
        } else {
            s = "." + s[:len(s)-2] // '¢' is 2 bytes
        }
        f, _ := strconv.ParseFloat(s, 64)
        res = append(res, f)
    }
    sort.Float64s(res)
    return res
}

// Gets a sorted slice of non-monetary integers.
func getNumbers(q string) []int {
    ns := rx3.FindAllString(q, -1)
    if ns == nil {
        return nil
    }
    var res []int
    for _, n := range ns {
        i, _ := strconv.Atoi(strings.TrimSpace(n))
        res = append(res, i)
    }
    sort.Ints(res)
    return res
}

// Gets the 'kinds' for the problem.
func getKinds(a []string) (int, []kind) {
    num, _ := strconv.Atoi(a[1])
    kinds := []kind{{a[2], 0, 0}, {a[5], 0, 0}}
    areCoins := false
    for i := range kinds {
        if v, ok := coins[kinds[i].name]; ok {
            kinds[i].value = v
            areCoins = true
        }
    }
    if !areCoins {
        return 0, nil
    }
    return num, kinds
}

// Checks if the problem involves 3 coins and
// also returns their names and the names of the coin which occurs most.
func hasThreeCoins(q string) ([]string, []string, bool) {
    q = strings.ReplaceAll(q, ".", "")
    q = strings.ReplaceAll(q, ",", "")
    words := strings.Split(q, " ")
    coinMap := make(map[string]int)
    for _, word := range words {
        if _, ok := coins[word]; ok {
            coinMap[word]++
        }
    }
    if len(coinMap) != 3 {
        return nil, []string{}, false
    }
    maxNum := 0
    var maxNames []string
    var names []string
    for k, v := range coinMap {
        names = append(names, k)
        if v > maxNum {
            maxNum = v
            maxNames = maxNames[:0]
            maxNames = append(maxNames, k)
        } else if v == maxNum {
            maxNames = append(maxNames, k)
        }
    }
    return names, maxNames, true
}

// Processes a problem which involves 3 coins.
func threeCoins(p, q string, names, maxNames []string) {
    var relations []relation
    am := rx4.FindAllStringSubmatch(q, -1)
    for i := 0; i < len(am); i++ {
        mult, kinds := getKinds(am[i])
        relations = append(relations, relation{kinds[0].name, kinds[1].name, float64(mult), 0})
    }
    mt := rx5.FindAllStringSubmatch(q, -1)
    for i := 0; i < len(mt); i++ {
        plus, kinds := getKinds(mt[i])
        relations = append(relations, relation{kinds[0].name, kinds[1].name, 1, float64(plus)})
    }
    lt := rx6.FindAllStringSubmatch(q, -1)
    for i := 0; i < len(lt); i++ {
        minus, kinds := getKinds(lt[i])
        relations = append(relations, relation{kinds[0].name, kinds[1].name, 1, -float64(minus)})
    }
    le := len(relations)
    if le > 2 {
        errorMsg(p)
        return
    }
    if le == 0 { // numbers of each coin must be the same
        sum := 0.0
        for _, name := range names {
            sum += coins[name]
        }
        res := getValues(q)
        tv := res[len(res)-1]
        n := int(tv/sum + 0.5)
        var kinds []kind
        for _, name := range names {
            kinds = append(kinds, kind{name, 0, n})
        }
        printAnswers(p, kinds)
    } else {
        res := getValues(q)
        totalValue := res[len(res)-1]
        for _, maxName := range maxNames {
            for i := 0; i < le; i++ {
                if relations[i].constant1 == 0 {
                    relations[i].constant1 = 0.5 // deals with 'one-half' cases
                }
                if le == 2 && maxName == relations[i].variable1 {
                    v := relations[i].variable2
                    relations[i].variable1, relations[i].variable2 = v, maxName
                    relations[i].constant1 = 1 / relations[i].constant1
                    relations[i].constant2 = -relations[i].constant2
                }
            }
            tv := totalValue
            var v1, v2, v3 string
            var n1, n2, n3 int
            if le == 2 {
                tmc := coins[relations[0].variable1]*relations[0].constant1 +
                    coins[relations[1].variable1]*relations[1].constant1 + coins[maxName]
                tv -= coins[relations[0].variable1]*relations[0].constant2 +
                    coins[relations[1].variable1]*relations[1].constant2
                v1, v2, v3 = maxName, relations[0].variable1, relations[1].variable1
                n1 = int(tv/tmc + 0.5)
                n2 = int(relations[0].constant1*float64(n1) + relations[0].constant2 + 0.5)
                n3 = int(relations[1].constant1*float64(n1) + relations[1].constant2 + 0.5)
            } else {
                res2 := getNumbers(q)
                tn := float64(res2[len(res2)-1])
                v1, v2 = relations[0].variable1, relations[0].variable2
                for _, name := range names {
                    if name != v1 && name != v2 {
                        v3 = name
                        break
                    }
                }
                mult1, mult2, mult3 := coins[v1], coins[v2], coins[v3]
                n2 = int(((tn-relations[0].constant2)*mult3-tv+relations[0].constant2*mult1)/
                    ((relations[0].constant1+1)*mult3-relations[0].constant1*mult1-mult2) + 0.5)
                n1 = int(float64(n2)*relations[0].constant1 + relations[0].constant2 + 0.5)
                n3 = int(tn) - n1 - n2
            }
            calcValue := float64(n1)*coins[v1] + float64(n2)*coins[v2] + float64(n3)*coins[v3]
            if math.Abs(totalValue-calcValue) <= 1e-14 {
                kinds := []kind{kind{v1, 0, n1}, kind{v2, 0, n2}, kind{v3, 0, n3}}
                printAnswers(p, kinds)
                return
            }
        }
        errorMsg(p)
    }
    return
}

func printAnswers(p string, kinds []kind) {
    fmt.Println(p)
    fmt.Print("ANSWER:")
    for i, kind := range kinds {
        if i > 0 {
            fmt.Print(",")
        }
        fmt.Printf(" %d %s", kind.number, kind.name)
    }
    fmt.Println("\n")
}

func errorMsg(p string) {
    fmt.Println(p)
    fmt.Println("*** CAN'T SOLVE THIS ONE ***\n")
}

func main() {
    ps := []string{
        "If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.",
        "A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.",
        "A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.",
        "A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.",
        "A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.",
        "In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.",
        "A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.",
        "A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.",
        "An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?",
        "A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?",
        "A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?",
        "A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?",
        "A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.",
        "A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.",
        "A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.",
        "A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.",
        "Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?",
        "A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?",
        "A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?",
        "Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?",
        "Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?",
        "In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?",
        "Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?",
        "A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?",
        "Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?",
        "Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?",
        "Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?",
        "A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?",
    }
    for _, p := range ps {
        q := strings.ToLower(p)
        q = strings.ReplaceAll(q, "twice", "two times")
        for _, d := range []string{"half", "one", "two", "five", "ten"} {
            q = strings.ReplaceAll(q, d+" dollar", d+"-dollar")
        }
        for k, v := range nums {
            q = strings.ReplaceAll(q, spaced(k), spaced(v))
        }
        for k, v := range nums2 {
            q = strings.ReplaceAll(q, k, v)
        }
        for k, v := range nums {
            q = strings.ReplaceAll(q, k+" ", v+" ")
        }
        for k, v := range bills {
            q = strings.ReplaceAll(q, k+" ", v+" ")
        }
        q = strings.ReplaceAll(q, " bills", "")
        q = strings.ReplaceAll(q, " bill", "")
        // check if there are 3 coins involved
        if names, maxNames, ok := hasThreeCoins(q); ok {
            threeCoins(p, q, names, maxNames)
            continue
        }
        am := rx4.FindAllStringSubmatch(q, -1)
        if len(am) == 1 {
            mult, kinds := getKinds(am[0])
            if kinds == nil {
                errorMsg(p)
                continue
            }
            res := getValues(q)
            tv := res[len(res)-1]
            fmult := float64(mult)
            kinds[1].number = int(tv/(fmult*kinds[0].value+kinds[1].value) + 0.5)
            kinds[0].number = kinds[1].number * mult
            printAnswers(p, kinds)
            continue
        }
        mt := rx5.FindAllStringSubmatch(q, -1)
        if len(mt) == 1 {
            plus, kinds := getKinds(mt[0])
            if kinds == nil {
                errorMsg(p)
                continue
            }
            res := getValues(q)
            tv := res[len(res)-1]
            fplus := float64(plus)
            kinds[1].number = int((tv-fplus*kinds[0].value)/(kinds[0].value+kinds[1].value) + 0.5)
            kinds[0].number = kinds[1].number + plus
            printAnswers(p, kinds)
            continue
        }
        lt := rx6.FindAllStringSubmatch(q, -1)
        if len(lt) == 1 {
            minus, kinds := getKinds(lt[0])
            if kinds == nil {
                errorMsg(p)
                continue
            }
            res := getValues(q)
            tv := res[len(res)-1]
            fminus := float64(minus)
            kinds[1].number = int((tv+fminus*kinds[0].value)/(kinds[0].value+kinds[1].value) + 0.5)
            kinds[0].number = kinds[1].number - minus
            printAnswers(p, kinds)
            continue
        }
        res := getValues(q)
        var tv float64
        if len(res) > 0 {
            tv = res[len(res)-1]
        } else {
            res3 := rx7.FindAllStringSubmatch(q, -1)
            i, _ := strconv.Atoi(res3[0][1])
            tv = float64(i)
        }
        res2 := getNumbers(q)
        tn := res2[len(res2)-1]
        coinNames := rx2.FindAllString(q, -1)
        sort.Strings(coinNames)
        var kinds []kind
        if len(coinNames) > 0 {
            kinds = append(kinds, kind{coinNames[0], coins[coinNames[0]], 0})
            for i := 1; i < len(coinNames); i++ {
                if coinNames[i] != coinNames[i-1] {
                    kinds = append(kinds, kind{coinNames[i], coins[coinNames[i]], 0})
                }
            }
            if len(kinds) != 2 {
                errorMsg(p)
                continue
            }
        } else if len(res) >= 3 {
            kinds = append(kinds, kind{fmt.Sprintf("$%.2f item", res[0]), res[0], 0})
            for i := 1; i < len(res)-1; i++ {
                if res[i] != res[i-1] {
                    kinds = append(kinds, kind{fmt.Sprintf("$%.2f item", res[i]), res[i], 0})
                }
            }
            if len(kinds) != 2 {
                errorMsg(p)
                continue
            }
        } else {
            errorMsg(p)
            continue
        }
        ftn := float64(tn)
        kinds[0].number = int((tv-ftn*kinds[1].value)/(kinds[0].value-kinds[1].value) + 0.5)
        kinds[1].number = tn - kinds[0].number
        printAnswers(p, kinds)
    }
}
Output:
If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.
ANSWER: 21 quarters, 7 dimes

A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.
ANSWER: 5 nickels, 13 pennies

A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.
ANSWER: 11 quarters, 5 nickels

A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.
ANSWER: 21 nickels, 11 quarters

A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
ANSWER: 7 pennies, 14 dimes, 10 nickels

In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.
ANSWER: 3 half-dollars, 9 quarters, 9 dimes

A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.
ANSWER: 5 $0.23 item, 7 $0.37 item

A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.
ANSWER: 32 $0.69 item, 48 $0.75 item

An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?
ANSWER: 7 $1.59 item, 2 $2.29 item

A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?
ANSWER: 5 five-dollar, 10 one-dollar, 4 ten-dollar

A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?
ANSWER: 5 dimes, 3 quarters

A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?
ANSWER: 3 nickels, 9 dimes, 8 pennies

A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.
ANSWER: 6 $1.50 item, 4 $2.00 item

A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.
ANSWER: 11 dimes, 2 nickels

A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.
ANSWER: 5 one-dollar, 15 two-dollar

A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
ANSWER: 17 nickels, 25 pennies, 20 dimes

Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
ANSWER: 14 one-dollar, 12 quarters

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
ANSWER: 18 nickels, 6 quarters, 9 dimes

A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
ANSWER: 9 pennies, 9 nickels, 9 dimes

Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
ANSWER: 8 dimes, 17 nickels

Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
ANSWER: 20 quarters, 18 dimes

In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?
ANSWER: 8 one-dollar, 2 ten-dollar, 3 five-dollar

Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?
ANSWER: 12 one-dollar, 4 five-dollar

A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?
ANSWER: 90 dimes, 45 nickels, 120 quarters

Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?
ANSWER: 15 dimes, 12 quarters

Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?
ANSWER: 140 nickels, 25 quarters

Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?
ANSWER: 121 quarters, 150 dimes

A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
ANSWER: 2 dimes, 10 pennies

Julia

Uses the JuMP optimization library as a solver. The examples are from the Go code, and a few regex are from the Perl code. 

using JuMP, GLPK

const nums = Dict(
    "zero"        => 0,   "one"       => 1,     "two"      => 2,    "three"    => 3,
    "four"        => 4,   "five"      => 5,     "six"      => 6,    "seven"    => 7,
    "eight"       => 8,   "nine"      => 9,     "ten"      => 10,   "eleven"   => 11,
    "twelve"      => 12,  "thirteen"  => 13,    "fourteen" => 14,   "fifteen"  => 15,
    "sixteen"     => 16,  "seventeen" => 17,    "eighteen" => 18,   "nineteen" => 19,
    "twenty"      => 20,
)

function coinproblemsolver(text, maxitems=4, verbose=false)
    coin_problem = Model(GLPK.Optimizer)
    for line in strip.(split(text, r"\n\n"))

        # save original version
        oldline = deepcopy(line)

        # ignore short or commented lines
        length(line) < 5 && continue
        line[1] == '#' && continue

        # create the data structures and registration function
        monies = Dict(
            "dollar_coin" => 100, "half_dollar" => 50, "quarter" => 25, "dime" => 10,
            "nickel" => 5, "penny" => 1,
        )
        foreach(d -> (monies["_" * "$d" * "_bill"] = 100 * d), [1, 2, 5, 10, 20, 50, 100, 500, 1000])

        itemnames = String[]
        itemvalues = Int[]

        function register_variables(vars)
            indices = Int[]
            for cap in vars
                idx = findfirst(x -> cap == x, itemnames)
                if !(idx isa Nothing)
                    push!(indices, idx)
                else
                    push!(itemnames, cap)
                    push!(indices, length(itemnames))
                    push!(itemvalues, get(monies, cap, 0))
                end
            end
            return indices
        end


        # set up the optimizer / problem solver
        @variables(coin_problem, begin x[1:maxitems] >= 0 end)


        # Simplify sentence and standardize quantities

        # convert hyphens to spaces, lowercase, newlines to spaces
        line = replace(replace(lowercase(line), "-" => " "), "\n" => " ")

        # fractions/multipliers to parsable forms
        line = replace(line, r"half.dollars?" => "half_dollar")
        line = replace(line, r"\bone\s+half\b" => "0.5")
        line = replace(line, r"\btwice\b" => "two times")

        # convert spelled out number to integer text per nums dictionary
        for p in nums
            line = replace(line, Regex("\\b" * p[1] * "\\b") => string(p[2]))
        end

        # remove plurals of coinage
        line = replace(line, r"(quarter|dime|nickel|dollar|coin|bill)s" => s"\1")
        line = replace(line, "pennies" => "penny")

        # change numerals to quantites and monies
        line = replace(line, r"dollar coin|all dollar" => "dollar_coin")
        line = replace(line, r"\$(\d+) bill" => s"_\1_bill")
        line = replace(line, r"(\d+) dollar bill" => s"_\1_bill")
        line = replace(line, r"((?:\d+\s+)+\d+)" => (s) -> mapreduce(x -> parse(Int, x), +, split(s))) # 20 6 -> 26

        # remove most unparsed words
        line = replace(line, r"\b(the|a|to|of|i|is|that|it|on|you|this|for|but|with|are|have|be|at|or|was|so|if|out|not|he|she|they|has|do|did|does)\b" => "")
        # simplify spacing
        line = replace(line, r"\s+" => " ")

        # Add variables and constraints to the problem
        for m in eachmatch(r"([\d\.]+) (?:times )?as many (\w+) as (\w+)", line)
            indices = register_variables([m[2], m[3]])
            @constraints(coin_problem, begin x[indices[1]] == x[indices[2]] * parse(Float64, m[1]) end)
        end
        for m in eachmatch(r"(\d+) more (\w+) than (\w+)", line)
            indices = register_variables([m[2], m[3]])
            @constraints(coin_problem, begin x[indices[1]] == x[indices[2]] + parse(Int, m[1]) end)
        end
        for m in eachmatch(r"(\d+) less (\w+) than (\w+)", line)
            indices = register_variables([m[2], m[3]])
            @constraints(coin_problem, begin x[indices[1]] == x[indices[2]] - parse(Int, m[1]) end)
        end
        if (m = match(r"same number (\w+), (\w+),? and (\w+)", line)) != nothing
            indices = register_variables(m.captures)
            @constraints(coin_problem, begin
                x[indices[1]] == x[indices[2]]
                x[indices[2]] == x[indices[3]]
            end)
        end
        if (m = match(r"(\d+) (?:\w+ )?(\w+),? consist\D+\$([\d\.]+)\D+\$([\d\.]+)", line)) != nothing
            n1, n2 = Int(round(100 * parse(Float64, m[3]))), Int(round(100 * parse(Float64, m[4])))
            s1, s2 = m[2] * "_costing_" * string(n1), m[2] * "_costing_" * string(n2)
            monies[s1], monies[s2] = n1, n2
            indices = register_variables([s1, s2])
            @constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
        end
        if (m = match(r"(\d+) (?:\w+ )?(\w+),? consist\D+([\d\.]+)¢\D+([\d\.]+)¢", line)) != nothing
            n1, n2 = parse(Int, m[3]), parse(Int, m[4])
            s1, s2 = m[2] * "_costing_" * string(n1), m[2] * "_costing_" * string(n2)
            monies[s1], monies[s2] = n1, n2
            indices = register_variables([s1, s2])
            @constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
        end
        if (m = match(r"(\d+) (?:coin|bill),? consist(?:s|ing) (\w+) and (\w+)", line)) != nothing
            indices = register_variables([m[2], m[3]])
            @constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
        end
        if (m = match(r"(\d+) (?:coin)[^\d\.,]+pocket (\w+) and (\w+)", line)) != nothing
            indices = register_variables([m[2], m[3]])
            @constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
        end
        if (m = match(r"(\d+) (?:coin|bill),? consist(?:s|ing) (\w+), (\w+), and (\w+)", line)) != nothing
            indices = register_variables([m[2], m[3], m[4]])
            @constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
        end
        if (m = match(r"\$([\d\.]+) ream\D+\$([\d\.]+)\D+(\d+) reams", line)) != nothing
            n1, n2 = Int(round(100 * parse(Float64, m[1]))), Int(round(100 * parse(Float64, m[2])))
            s1, s2 = "ream_costing_" * string(n1), "ream_costing_" * string(n2)
            monies[s1], monies[s2] = n1, n2
            indices = register_variables([s1, s2])
            @constraints(coin_problem, begin sum(x) == parse(Int, m[3]) end)
        end
        if (m = match(r"(?:in my wallet,?|only accepts) (\w+), (\w+),? and (\w+)", line)) != nothing
            indices = register_variables([m.captures[1], m.captures[2], m.captures[3]])
        end
        if (m = match(r"(\d+) coin in (\w+) and (\w+) only", line)) != nothing
            indices = register_variables([m.captures[2], m.captures[3]])
            @constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
        end
        if (m = match(r"(\d+) coin (?:total|in all)", line)) != nothing
            @constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
        end
        if (m = match(r"(?:had only|in) (\w+) and (\w+)[,\.\?]", line)) != nothing
            indices = register_variables([m.captures[1], m.captures[2]])
        end
        if (m = match(r"(?:sold total|all together,? there) (\d+)", line)) != nothing
            @constraints(coin_problem, begin sum(x) == parse(Int, m[1]) end)
        end
        for m in eachmatch(r"cost \$([\d\.]+) each", line)
            s = "item_costing_" * m.captures[1]
            monies[s] = Int(round(100 * parse(Float64, m.captures[1])))
            register_variables([s])
        end

        # find a total
        m = match(r"add up \$?([\d\.]+)", line)
        if m isa Nothing
            m = match(r"(?:cost stamps|total cost|paid|value|valuing|store made)[^\$]+\$([\d\.]+)", line)
        end
        if m isa Nothing
            m = match(r"(?:total|value of|store made|given)[^\$]+\$([\d\.]+)", line)
        end
        if m isa Nothing
            m = match(r"\$([\d\.]+) (?:coin )?in", line)
        end
        if !(m isa Nothing)
            m1 = m.captures[1][end] == '.' ? m.captures[1][1:end-1] : m.captures[1]
            @constraints(coin_problem, begin
                sum([itemvalues[i] * x[i] for i in 1:length(itemnames)]) == Int(round(100 * parse(Float64, m1)))
            end)
        else
            m = match(r"total (?:amount coin )([\d\.]+)¢", line)
            if !(m isa Nothing)
                @constraints(coin_problem, begin
                    sum([itemvalues[i] * x[i] for i in 1:length(itemnames)]) == parse(Int, m[1])
                end)
            else
                error("Missing or unparsed total funds constraint")
            end
        end


        # set unused x components to 0
        for i in length(itemnames)+1:maxitems
            @constraints(coin_problem, begin x[i] == 0 end)
        end

        # solve
        optimize!(coin_problem)
        verbose && println(line)
        verbose && println(coin_problem)
        print(oldline, "\nAnswer:   ")
        for i in eachindex(itemnames)
            print(rpad(itemnames[i] * "(s)", 10), ": ", rpad(Int(round(JuMP.value(x[i]))), 10))
        end
        println("\n")
        JuMP.empty!(coin_problem)
    end
end

const DATA =  raw"""
If a person has three times as many quarters as dimes and the total amount of money is $5.95,
find the number of quarters and dimes.

A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢,
find the number of pennies and nickels.

A small child has 6 more quarters than nickels. If the total amount of coins is $3.00,
find the number of nickels and quarters the child has.

A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of
money is $3.80, find the number of nickels and quarters in the bank.

A person has twice as many dimes as she has pennies and three more nickels than pennies. If
the total amount of the coins is $1.97, find the numbers of each type of coin the person has.

In a bank, there are three times as many quarters as half dollars and 6 more dimes than
half dollars. If the total amount of the money in the bank is $4.65, find the number of
each type of coin in the bank.

A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps
is $3.74, find the number of each type of the stamps purchased.

A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches
cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number
of each sold.

An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled
notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and
paid $15.71, how many reams of each type of paper did the student purchase?

A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are
twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each
type of bill are there?

A person has 8 coins consisting of quarters and dimes. If the total amount of this change
is $1.25, how many of each kind of coin are there?

A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the
total amount of these coins is $1.13, how many of each kind of coin does he have?

A person bought ten greeting cards consisting of birthday cards costing $1.50 each and
anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the
number of each kind of card the person bought.

A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the
number of dimes the person has.

A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money
the person has is $35, find the number of $2 bills the person has.

A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total
amount of money in the bank is $3.10, find the number of dimes in the bank.

Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you
can have all the coins if you can figure out how many of each kind of coin he is carrying.
You're not too interested until he tells you that he's been collecting those gold-tone
one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they
add up to seventeen dollars in value. How many of each coin does he have?

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30.
If there are three times as many nickels as quarters, and one-half as many dimes as nickels,
how many coins of each kind are there?

A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How
many of each type of coin does the wallet contain?

Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of
each coin does he have?

Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes
is 38. How many quarters and dimes does Terry have?

In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total
amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills.
All together, there are 13 bills in my wallet. How many of each bill do I have?

Marsha has three times as many one-dollar bills as she does five dollar bills. She has a
total of $32. How many of each bill does she have?

A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts
nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin
are in the machine?

Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins
of each kind did he have?

Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each
type of coin did she have?

Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each
type of coin does he have?

A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30,
how many of each coin are there?
"""

coinproblemsolver(DATA)
Output:
If a person has three times as many quarters as dimes and the total amount of money is $5.95, 
find the number of quarters and dimes.
Answer:   quarter(s): 21        dime(s)   : 7

A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, 
find the number of pennies and nickels.
Answer:   penny(s)  : 13        nickel(s) : 5

A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, 
find the number of nickels and quarters the child has.
Answer:   quarter(s): 11        nickel(s) : 5

A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of 
money is $3.80, find the number of nickels and quarters in the bank.
Answer:   nickel(s) : 21        quarter(s): 11

A person has twice as many dimes as she has pennies and three more nickels than pennies. If
the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
Answer:   dime(s)   : 14        penny(s)  : 7         nickel(s) : 10

In a bank, there are three times as many quarters as half dollars and 6 more dimes than
half dollars. If the total amount of the money in the bank is $4.65, find the number of
each type of coin in the bank.
Answer:   quarter(s): 9         half_dollar(s): 3         dime(s)   : 9

A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps 
is $3.74, find the number of each type of the stamps purchased.
Answer:   stamps_costing_37(s): 7         stamps_costing_23(s): 5

A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches
cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number
of each sold.
Answer:   item_costing_0.69(s): 32        item_costing_0.75(s): 48

An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled
notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and
paid $15.71, how many reams of each type of paper did the student purchase?
Answer:   ream_costing_159(s): 7         ream_costing_229(s): 2

A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are 
twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each
type of bill are there?
Answer:   _1_bill(s): 10        _5_bill(s): 5         _10_bill(s): 4

A person has 8 coins consisting of quarters and dimes. If the total amount of this change
is $1.25, how many of each kind of coin are there?
Answer:   quarter(s): 3         dime(s)   : 5

A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the
total amount of these coins is $1.13, how many of each kind of coin does he have?
Answer:   dime(s)   : 9         nickel(s) : 3         penny(s)  : 8

A person bought ten greeting cards consisting of birthday cards costing $1.50 each and
anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the
number of each kind of card the person bought.
Answer:   cards_costing_150(s): 6         cards_costing_200(s): 4

A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the
number of dimes the person has.
Answer:   dime(s)   : 11        nickel(s) : 2

A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money
the person has is $35, find the number of $2 bills the person has.
Answer:   _1_bill(s): 5         _2_bill(s): 15

A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total
amount of money in the bank is $3.10, find the number of dimes in the bank.
Answer:   penny(s)  : 25        nickel(s) : 17        dime(s)   : 20

Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you 
can have all the coins if you can figure out how many of each kind of coin he is carrying.
You're not too interested until he tells you that he's been collecting those gold-tone
one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they
add up to seventeen dollars in value. How many of each coin does he have?
Answer:   dollar_coin(s): 14        quarter(s): 12

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30.
If there are three times as many nickels as quarters, and one-half as many dimes as nickels,
how many coins of each kind are there?
Answer:   nickel(s) : 18        quarter(s): 6         dime(s)   : 9

A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How 
many of each type of coin does the wallet contain?
Answer:   penny(s)  : 9         nickel(s) : 9         dime(s)   : 9

Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of
each coin does he have?
Answer:   nickel(s) : 17        dime(s)   : 8

Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes
is 38. How many quarters and dimes does Terry have?
Answer:   quarter(s): 20        dime(s)   : 18

In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total
amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills.
All together, there are 13 bills in my wallet. How many of each bill do I have?
Answer:   _1_bill(s): 8         _10_bill(s): 2         _5_bill(s): 3

Marsha has three times as many one-dollar bills as she does five dollar bills. She has a
total of $32. How many of each bill does she have?
Answer:   _1_bill(s): 12        _5_bill(s): 4

A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts
nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin
are in the machine?
Answer:   dime(s)   : 90        nickel(s) : 45        quarter(s): 120       

Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins
of each kind did he have?
Answer:   quarter(s): 12        dime(s)   : 15

Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each
type of coin did she have?
Answer:   nickel(s) : 140       quarter(s): 25

Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each
type of coin does he have?
Answer:   quarter(s): 121       dime(s)   : 150

A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30,
how many of each coin are there?
Answer:   dime(s)   : 2         penny(s)  : 10

Perl

Coin-type 'word problems' are analyzed into their constituent algebraic relationships, in a format suitable for processing by MAXIMA, a free computer algebra system. NB: MAXIMA must be locally installed for this task to function. 

use strict;
use warnings;

use List::Util qw(sum uniq);
use File::Temp qw(tempfile);

my %nums = (
        zero        => 0,   one       => 1,     two      => 2,    three    => 3,
        four        => 4,   five      => 5,     six      => 6,    seven    => 7,
        eight       => 8,   nine      => 9,     ten      => 10,   eleven   => 11,
        twelve      => 12,  thirteen  => 13,    fourteen => 14,   fifteen  => 15,
        sixteen     => 16,  seventeen => 17,    eighteen => 18,   nineteen => 19,
        twenty      => 20,
);

my $decimal = qr/(?:[1-9][0-9]*\.?[0-9]*)|(?:0?\.[0-9]+)/;

while (<DATA>) {
    chomp;
    next if /^\s*$/ or /^\s*#.*$/; # skip blank and comment lines 

    my($count, $total) = (0, 0);
    our @words = our @eqns = our @vars = our @types = ();

    sub add_type {
        my($type,$value) = @_;
        push @vars, "v_$type: $value";
        push @types, $type;
    }

    # Step 1: standardize language

    s/-/ /g;                       # convert hyphens to spaces
    $_ = lc($_);                   # convert to lower case

    # tokenize sentence boundaries, punctuation, symbols
    s/([\.\?\!]) / $1\n/g;
    s/([\.\?\!])$/ $1\n/g;
    s/\$(.)/\$ $1/g;               # prefix
    s/(.)([\;\:\%',¢])/$1 $2/g;    # suffix

    # fractions/multipliers
    s/half.dollars?/half_dollar/g;
    s/\b(one )?half\b/0.5/g;
    s/\btwice\b/two times/g;

    # convert English number-names to numbers
    foreach my $key (keys %nums) { s/\b$key\b/$nums{$key}/eg }

    # remove plurals
    s/(quarter|dime|nickel|dollar|coin|bill)s/$1/g;
    s/pennies/penny/g;

    # misc
    s/dollar coin/dollar_coin/g;
    s/(\d+) dollar\b/\$ $1/g;
    s/((?:\d+ )*\d+)/sum(split(' ',$1))/eg;

    # remove non-essential words
    s/\b(the|a|to|of|i|is|that|it|on|you|this|for|but|with|are|have|be|at|or|was|so|if|out|not|he|she|they|has|do|did|does)\b\s*//g;

    # Step 2: assign numeric values to terms

    add_type('dollar_coin',100) if /dollar_coin/;
    add_type('half_dollar',50)  if /half_dollar/;
    add_type('quarter',25)      if /quarter/;
    add_type('dime',10)         if /dime/;
    add_type('nickel',5)        if /nickel/;
    add_type('penny',1)         if /penny/;
    add_type($1, 100 * $1) while /\$ (\d+) bill/g;

    # Step 3: determine algebraic relationships

    while (/($decimal) (?:times )?as many \$ (\d+) bill as \$ (\d+) bill/g) { push @eqns, "n_$2 = n_$3 * $1" }
    while (/($decimal) (?:times )?as many (\w+) as (\w+)/g)                 { push @eqns, "n_$2 = n_$3 * $1" }
    while (/(\d+) more (\w+) than (\w+)/g)                                  { push @eqns, "n_$2 = n_$3 + $1" }
    while (/(\d+) less (\w+) than (\w+)/g)                                  { push @eqns, "n_$2 = n_$3 - $1" }
    while (/(\d+) less \$ (\d+) bill than \$ (\d+) bill/g)                  { push @eqns, "n_$2 = n_$3 - $1" }

    if (/same number (\w+) , (\w+) (?:, )?and (\w+)/) {
        push @eqns, "n_$1 = n_$2";
        push @eqns, "n_$2 = n_$3";
    }

    if (/(\d+) (?:\w+ )*consists/ or /(?<!\$ )(\d+) coin/ or /[^\$] (\d+) bill/) {
        $count = $1; push @vars, "count: $count"
    }

    if (/total (?:\w+ )*\$ ($decimal)/ or /valu(?:e|ing) \$ ($decimal)/ or /\$ ($decimal) ((bill|coin) )?in/) {
        $total = 100 * $1;
        push @vars, "total: $total";
    }

    if (/total (?:\w+ )*($decimal)/) {
        $total = $1;
        push @vars, "total: $total";
    }

    # Step 4: tally final total value, coin count

    # sum total, dot product of values and quantities
    my $dot_product = join(' + ', map {"n_$_ * v_$_"} uniq @types);
    push @eqns, "total = $dot_product" if $total and @types;

    # count of all coins, sum of counts of each coin type
    my $trace = join(' + ', map {"n_$_"} uniq @types);
    push @eqns, "count = $trace" if $count and @types;

    # Step 5: prepare batch file for external processing, run 'MAXIMA', output results

    printf "problem: %s\n", s/\n/ /gr;  # condensed problem statement

    my $maxima_vars = join("\$\n", uniq @vars);
    my $maxima_eqns = '['. join(', ', @eqns) . ']';
    my $maxima_find = '['. join(', ', map {"n_$_"} @types) . ']';

    if (@eqns and @vars) {
        my ($fh, $maxima_script) = tempfile(UNLINK => 1);
        open $fh, '>', $maxima_script or die "Couldn't open temporary file: $!\n";
        print $fh <<~"END";
            $maxima_vars\$
            solve($maxima_eqns, $maxima_find);
            END
        close $fh;

        open my $maxima_output, "/opt/local/bin/maxima -q -b $maxima_script |" or die "Couldn't open maxima: $!\n";
        while (<$maxima_output>) {
            print "solution: $1\n" if /\(\%o\d+\)\s+\[\[([^\]]+)\]\]/; # only display solution
        }
        close  $maxima_output;
 
    } else {
        print "Couldn't deduce enough information to formulate equations.\n"
    }
    print "\n";
}

__DATA__
If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.

A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.

A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.

A childs bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.

A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.

In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.

A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?

A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?

A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?

A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.

A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.

A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.

The twenty-six coins in my pocket are all dollar coins and quarters, and they add up to seventeen dollars in value. How many of each coin are there?

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?

A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?

Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?

Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?

In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?

Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?

A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine.

Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?

Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?

Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?

A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
Output:
problem: person 3 times as many quarter as dime and total amount money $ 5.95 , find number quarter and dime .
solution: n_quarter = 21, n_dime = 7

problem: pile 18 coin consists penny and nickel . total amount coin 38 ¢ , find number penny and nickel .
solution: n_nickel = 5, n_penny = 13

problem: small child 6 more quarter than nickel . total amount coin $ 3.0 , find number nickel and quarter child .
solution: n_quarter = 11, n_nickel = 5

problem: childs bank contains 32 coin consisting nickel and quarter . total amount money $ 3.80 , find number nickel and quarter in bank .

solution: n_quarter = 11, n_nickel = 21

problem: person 2 times as many dime as penny and 3 more nickel than penny . total amount coin $ 1.97 , find numbers each type coin person .
solution: n_dime = 14, n_nickel = 10, n_penny = 7

problem: in bank , 3 times as many quarter as half_dollar and 6 more dime than half_dollar . total amount money in bank $ 4.65 , find number each type coin in bank .
solution: n_half_dollar = 3, n_quarter = 9, n_dime = 9

problem: clerk given $ 75 in bill put in cash drawer start workday . 2 times as many $ 1 bill as $ 5 bill and 1 less $ 10 bill than $ 5 bill . how many each type bill ?
solution: n_1 = 10, n_10 = 4, n_5 = 5

problem: person 8 coin consisting quarter and dime . total amount change $ 1.25 , how many each kind coin ?
solution: n_quarter = 3, n_dime = 5

problem: person 3 times as many dime as nickel and 5 more penny than nickel . total amount these coin $ 1.13 , how many each kind coin ?
solution: n_dime = 9, n_nickel = 3, n_penny = 8

problem: person 9 more dime than nickel . total amount money $ 1.20 , find number dime person .
solution: n_dime = 11, n_nickel = 2

problem: person 20 bill consisting $ 1 bill and $ 2 bill . total amount money person $ 35 , find number $ 2 bill person .
solution: n_1 = 5, n_2 = 15

problem: bank contains 8 more penny than nickel and 3 more dime than nickel . total amount money in bank $ 3.10 , find number dime in bank .
solution: n_dime = 20, n_nickel = 17, n_penny = 25

problem: 26 coin in my pocket all dollar_coin and quarter , and add up $ 17 in value . how many each coin ?
solution: n_dollar_coin = 14, n_quarter = 12

problem: collection 33 coin , consisting nickel , dime , and quarter , value $ 3.30 . 3 times as many nickel as quarter , and 0.5 as many dime as nickel , how many coin each kind ?
solution: n_quarter = 6, n_dime = 9, n_nickel = 18

problem: wallet contains same number penny , nickel , and dime . coin total $ 1.44 . how many each type coin wallet contain ?
solution: n_dime = 9, n_nickel = 9, n_penny = 9

problem: suppose ken 25 coin in nickel and dime only and total $ 1.65 . how many each coin ?
solution: n_dime = 8, n_nickel = 17

problem: terry 2 more quarter than dime and total $ 6.80 . number quarter and dime 38 . how many quarter and dime terry ?
solution: n_quarter = 20, n_dime = 18

problem: in my wallet , $ 1 bill , $ 5 bill , and $ 10 bill . total amount in my wallet $ 43 . 4 times as many $ 1 bill as $ 10 bill . all together , 13 bill in my wallet . how many each bill ?
solution: n_5 = 3, n_1 = 8, n_10 = 2

problem: marsha 3 times as many $ 1 bill as $ 5 bill . total $ 32 . how many each bill ?
solution: n_1 = 12, n_5 = 4

problem: vending machine $ 41.25 in . 255 coin total and machine only accepts nickel , dime and quarter . 2 times as many dime as nickel . how many each coin in machine .
solution: n_quarter = 120, n_dime = 90, n_nickel = 45

problem: michael had 27 coin in all , valuing $ 4.50 . had only quarter and dime , how many coin each kind ?
solution: n_quarter = 12, n_dime = 15

problem: lucille had $ 13.25 in nickel and quarter . had 165 coin in all , how many each type coin ?
solution: n_quarter = 25, n_nickel = 140

problem: ben $ 45.25 in quarter and dime . 29 less quarter than dime , how many each type coin ?
solution: n_quarter = 121, n_dime = 150

problem: person 12 coin consisting dime and penny . total amount money $ 0.30 , how many each coin ?
solution: n_dime = 2, n_penny = 10

Phix

The title of this task is solving coin problems, therefore I have ruthlessly eradicated stamps, sandwiches, paper, and cards. It just adds unnecessary fiddling, along with the need to add custom assets and asset-values, such as 37c stamps, $1.50 cards, etc. Hence this covers 24/28 of the Perl/Go examples. On the plus side, there is no hard limit on the number of unknowns, though all examples below are for 2 and 3 only. A couple (14 and 17) also sail perilously close to getting a divide by zero. This task was quite a bit of fun, once I got stuck in. 

-- demo\rosetta\Solving_coin_problems.exw
with javascript_semantics
constant source = """
If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.
--==>expected:quarters = 21, dimes = 7
A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38c, find the number of pennies and nickels.
--==>expected:pennies = 13, nickels = 5
A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.
--==>expected:quarters = 11, nickels = 5
A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.
--==>expected:nickels = 21, quarters = 11
A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
--==>expected:dimes = 14, pennies = 7, nickels = 10
In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.
--==>expected:quarters = 9, half_dollars = 3, dimes = 9
A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?
--==>expected:one_dollar_bills = 10, five_dollar_bills = 5, ten_dollar_bills = 4
A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?
--==>expected:quarters = 3, dimes = 5
A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?
--==>expected:dimes = 9, nickels = 3, pennies = 8
A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.
--==>expected:dimes = 11, nickels = 2
A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.
--==>expected:one_dollar_bills = 5, two_dollar_bills = 15
A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
--==>expected:pennies = 25, nickels = 17, dimes = 20
Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
--==>expected:dollars = 14, quarters = 12
A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
--==>expected:nickels = 18, dimes = 9, quarters = 6
A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
--==>expected:pennies = 9, nickels = 9, dimes = 9
Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
--==>expected:nickels = 17, dimes = 8
Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
--==>expected:quarters = 20, dimes = 18
In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?
--==>expected:one_dollar_bills = 8, five_dollar_bills = 3, ten_dollar_bills = 2
Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?
--==>expected:one_dollar_bills = 12, five_dollar_bills = 4
A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine.
--==>expected:nickels = 45, dimes = 90, quarters = 120
Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?
--==>expected:quarters = 12, dimes = 15
Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?
--==>expected:nickels = 140, quarters = 25
Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?
--==>expected:quarters = 121, dimes = 150
A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
--==>expected:dimes = 2, pennies = 10""",

{texts,replacements} = columnize({{"."," ."},
                                  {","," ,"},
                                  {"had","has"},
                                  {"contain?","have?"},
                                  {"there?","have?"},
                                  {"has .","have?"},
                                  {"in the bank .","have?"},
                                  {"in the machine .","have?"},
                                  {"as many","asmany"},
                                  {" , and they add up"," . total"},
                                  {" , has a value"," . total"},
                                  {" only and has a total"," . total"},
                                  {" and has a total"," . total"},
                                  {"All together ,","total"},
                                  {"A vending machine has","total"},
                                  {"valuing","total"},
                                  {"coins in all ,","coins ."},
                                  {"coins total and","coins ."},
                                  {"find","many"},
                                  {"consists","consisting"},
                                  {"twenty-six","26"},
                                  {"seventeen dollars in value","$17.00"},
                                  {" one "," 1 "},
                                  {"three","3"},
                                  {"four","4"},
                                  {"twice","2 times"},
                                  {"ten","10"},
                                  {" and the total"," . total"},
                                  {"half dollars","half_dollars"},
                                  {"$1 bills","one_dollar_bills"},
                                  {"$2 bills","two_dollar_bills"},
                                  {"$5 bills","five_dollar_bills"},
                                  {"$10 bill","ten_dollar_bills"},
                                  {"one-dollar bills","one_dollar_bills"},
                                  {"five-dollar bills","five_dollar_bills"},
                                  {"five dollar bills","five_dollar_bills"},
                                  {"10-dollar bills","ten_dollar_bills"},
                                  {"10_dollar_bills","ten_dollar_bills"}}),

noise = split("the|a|to|of|i|is|that|it|on|you|this|for|but|with|are|have|be|at|or|was|so|if|out|not|he|she|they|has|do|does"&
              "|in|these|person|small|child|child's|bank|pile|clerk|given|put|there|cash|drawer|start|workday|his|suppose|ken"&
              "|terry|how|my|marsha|machine|accepts|michael|lucille|ben|number|type|kind|amount|collection|contains|change"&
              "|wallet|did|numbers|pocket","|"),

-- one spectacularly irksome preamble containing absolutely no useful information whatsoever...:
uncle = "your uncle walks in , jingling the coins in his pocket . "&
        "he grins at you and tells you that you can have all the coins "&
        "if you can figure out how many of each kind of coin he is carrying . "&
        "you're not too interested until he tells you that he's been collecting "&
        "those gold-tone one-dollar coins . ",

vocab = {"times","asmany","quarters","as","dimes","and","total","money","many","have?",
         "coins","consisting","pennies","nickels","more","less","than","each","coin",
         "half_dollars","bills","bill","all","dollars","one-half","same","only",
         "one_dollar_bills","two_dollar_bills","five_dollar_bills","ten_dollar_bills"},

{assets,assetv} = columnize({{"ten_dollar_bills",1000},
                             {"five_dollar_bills",500},
                             {"two_dollar_bills",200},
                             {"one_dollar_bills",100},
                             {"dollars",100},
                             {"half_dollars",50},
                             {"quarters",25},
                             {"dimes",10},
                             {"nickels",5},
                             {"pennies",1}})

integer count = 0
sequence lines = split(substitute_all(source,texts,replacements),"\n"),
         expectations = {},
         vused = repeat(false,length(vocab))
procedure cleanup_lines()
    sequence words
    for i=1 to length(lines) by 2 do
        string li = lower(lines[i])
        if match("your uncle",li)=1 then
            -- note: if you tweak texts/replacements then you may
            --       need to tweak the uncle constant to match.
            if match(uncle,li)!=1 then ?9/0 end if
            li = li[length(uncle)+1..$]
        end if
        words = split(li)
        for n=1 to length(noise) do
            words = remove_all(noise[n],words)
        end for
        if words[$]="." and find(words[$-1],{"dimes","nickels"}) then
            words[$] = "have?"
        end if
        if words[1]="," then words = words[2..$] end if
        for w=length(words) to 2 by -1 do
            -- re-join eg "$3" and ".99" (oops)
            if length(words[w])>1 and words[w][1]='.' then
                words[w-1..w] = {words[w-1]&words[w]}
            end if
        end for
        words = match_replace({",","many"},words,{".","many"})
        words = match_replace({","},words,{})
        count += 1
        lines[count] = words
        li = lines[i+1]
        if match("--==>expected:",li)!=1 then ?9/0 end if
        li = li[15..$]
        li = substitute(li," ,",",")
        expectations = append(expectations,li)
    end for
    lines = lines[1..count]
    printf(1,"%d puzzles:\n",count)
    printf(1,"Step 1: remove noise and otherwise simplify (if nothing else, down to a %d-word vocab):\n\n",length(vocab))
    for i=1 to count do
        printf(1,"%d: %s\n",{i,join(lines[i])})
    end for
end procedure 
cleanup_lines()

function add_unknowns(sequence unknowns, words)
    for i=1 to length(words) do
        string word = words[i]
        if not find(word,unknowns)
        and not find(word,{"as","consisting","all","and","than","only"}) then
            unknowns = append(unknowns,word)
        end if
    end for
    return unknowns
end function

function parse_sentence(sequence words, unknowns)
-- Converts eg {"$1.00","quarters","and","nickels"} to {100,25,5}.
-- An "equation" of {100,25,5} means "100==25*unknown[1]+5*unknown[2]".
-- Obviously this is suitably scruffy, but the 31-word vocab certainly helps!
-- It is worth noting that by this stage most sentences begin or end in a number.
-- Since we may not have the full set of unknowns, each equation ends with a code:
-- 0: pad with 0, 1: pad with 1, 'a': pad with the unknown asset values
sequence sentences = {},
         sentence,
         rest = {},
         isnumber = repeat(0,length(words))
integer k
bool set_asset_sum = false
    unknowns = deep_copy(unknowns)
    for w=1 to length(words) do
        string ww = words[w]
        k = find(ww,vocab)
        if k=0 then
            sequence r
            for f=1 to 3 do
                r = scanf(ww,{"%d","%dc","$%f"}[f])
                if r!={} then
                    isnumber[w] = iif(f=3?round(r[1][1]*100):r[1][1])
                    exit
                end if
            end for
            if r={} then ?ww ?9/0 end if
        else
            vused[k] = true
        end if
    end for
    if isnumber[1] then
        if words[2]="times" then
            if words[3]!="asmany" then ?9/0 end if
            k = find("and",words)
            if k then
                rest = words[k+1..$]
                words = words[1..k-1]
            end if
            -- eg {"3","times","asmany","quarters","as","dimes"}
            if length(words)!=6 or words[5]!="as" then ?9/0 end if
            unknowns = add_unknowns(unknowns, words[4..6])
            sentence = repeat(0,length(unknowns)+1)
            k = find(words[4],unknowns)
            sentence[k+1] = 1
            k = find(words[6],unknowns)
            sentence[k+1] = -isnumber[1]
            sentence &= 0
            sentences = append(sentences,sentence)
        elsif words[2]="coins"
           or (words[2]="bills" and length(words)>2) then
            --/* eg:
                {"18","coins","consisting","pennies","and","nickels"}
                {"26","coins","all","dollars","and","quarters"}
                {"25","coins","nickels","and","dimes"}
                {"33","coins","consisting","nickels","dimes","and","quarters"}
                {"27","coins"}
                {"20","bills","consisting","one_dollar_bills","and","two_dollar_bills"}
            --*/
            unknowns = add_unknowns(unknowns, words[3..$])
            sentence = {isnumber[1]}&repeat(1,length(unknowns))
            sentence &= 1
            sentences = append(sentences,sentence)
        elsif find(words[2],{"more","less"}) then
            k = find("and",words)
            if k then
                rest = words[k+1..$]
                words = words[1..k-1]
            end if
            --/* eg:
                {"5","more","pennies","than","nickels"}
                {"29","less","quarters","than","dimes"}
            --*/
            if length(words)!=5 or words[4]!="than" then ?9/0 end if
            unknowns = add_unknowns(unknowns, words[3..$])
            sentence = {isnumber[1]}&repeat(0,length(unknowns))
            integer less = iff(words[2]="less"?-1:+1)
            k = find(words[3],unknowns)
            sentence[k+1] = less
            k = find(words[5],unknowns)
            sentence[k+1] = -less
            sentence &= 0
            sentences = append(sentences,sentence)
        else
            --/* eg:
                {"$75","bills"}
                {"$45.25","quarters","and","dimes"}
            --*/
            if length(words)>2 then
                -- log assets:
                -- eg {"$13.25","nickels","and","quarters"}
                if words[3]!="and" or length(words)!=4 then ?9/0 end if
                unknowns = add_unknowns(unknowns, words[2..$])
            end if
            sentence = {isnumber[1]}
            set_asset_sum = true
        end if
    elsif isnumber[$] then
        if words[1]="total"
        or (length(words)=3 and words[1..2]={"coins","total"}) then
            --/*
                {"total","money","$5.95"}
                {"total","coins","38c"}
                {"total","coins","$3.00"}
                {"total","$3.74"}
                {"total","cost","$17.00"}
                {"coins","total","$1.44"}
            --*/
            sentence = {isnumber[$]}
            set_asset_sum = true
        else
            -- eg {"quarters","and","dimes","38"}
            unknowns = add_unknowns(unknowns, words[1..$-1])
            sentence = {isnumber[$]}&repeat(1,length(unknowns))
            sentence &= 1
            sentences = append(sentences,sentence)
        end if
    elsif words[1]="one-half" then
        -- eg {"one-half","asmany","dimes","as","nickels"}
        if length(words)!=5 or words[2]!="asmany" or words[4]!="as" then ?9/0 end if
        unknowns = add_unknowns(unknowns, words[3..$])
        sentence = repeat(0,length(unknowns)+1)
        k = find(words[3],unknowns)
        sentence[k+1] = -2
        k = find(words[5],unknowns)
        sentence[k+1] = 1
        sentence &= 0
        sentences = append(sentences,sentence)
    elsif words[1]="many" then
        --/* eg
            {"many","quarters","and","dimes","have?"}
            {"many","each","coin","have?"}
            {"many","each","have?"}
            {"many","each","bill","have?"}
            {"many","dimes","have?"}
            {"many","coins","each","have?"}
        --*/
        if words[$]!="have?" then ?9/0 end if
        -- no rule, as yet, just outputs everything instead.
    elsif words[1]="same" then
        -- eg {"same","pennies","nickels","and","dimes"}
        unknowns = add_unknowns(unknowns, words[2..$])
        if length(unknowns)!=3 then ?9/0 end if
        sentences = append(sentences,{0,1,-1,0,0})  -- (p==n)
        sentences = append(sentences,{0,0,1,-1,0})  -- (n==d)
    elsif words[1]="total" then
        -- eg {"total","13","bills"}
        if length(words)!=3 or not isnumber[2] or words[3]!="bills" then ?9/0 end if
        sentence = {isnumber[2]}&repeat(1,length(unknowns))
        sentence &= 1
        sentences = append(sentences,sentence)
    else
        --/* eg:
            {"one_dollar_bills","five_dollar_bills","and","ten_dollar_bills"}
            {"only","nickels","dimes","and","quarters"}
            {"only","quarters","and","dimes"}
        --*/
        -- just log assets:
        unknowns = add_unknowns(unknowns, words)
    end if
    if set_asset_sum then
        -- common code for eg {"total","$3.74"} and {"$75","bills"}
        for u=1 to length(unknowns) do
            string uu = unknowns[u]
            k = find(uu,assets)
            sentence &= assetv[k]
        end for
        sentence &= 'a'
        sentences = append(sentences,sentence)
    end if
    if length(rest) then
--      {sequence s2,unknowns} = parse_sentence(rest,unknowns)
        sequence s2
        {s2,unknowns} = parse_sentence(rest,unknowns)
        sentences &= s2
    end if
    return {sentences,unknowns}
end function

procedure solveN(integer n, sequence rules, unknowns, string expected)
--
-- Based on https://mathcs.clarku.edu/~djoyce/ma105/simultaneous.html
--  aka the ancient Chinese Jiuzhang suanshu ~100 B.C. (!!)
--
-- Example (ignoring n, which is solely for output):
--  rules = {{18,1,1},{38,1,5}}, ie 18==p+n, 38==p+5*n
--  unknowns = {"pennies","nickels"}
--  expected = "pennies = 13, nickels = 5"
--
--  In the elimination phase, both p have multipliers of 1, so we can
--  ignore those two sq_mul and just do (38=p+5n)-(18=p+n)==>(20=4n).
--  Obviously therefore n is 5 and substituting backwards p is 13.
--
    string res
    sequence sentences = rules, ri, rj
    integer l = length(rules), rii, rji
    rules = deep_copy(rules)
    for i=1 to l do
        -- successively eliminate (grow lower left triangle of 0s)
        ri = rules[i]
        if length(ri)!=l+1 then ?9/0 end if
        rii = ri[i+1]
        if rii=0 then ?9/0 end if
        for j=i+1 to l do
            rj = rules[j]
            rji = rj[i+1]
            if rji!=0 then
                rj = sq_sub(sq_mul(rj,rii),sq_mul(ri,rji))
                if rj[i+1]!=0 then ?9/0 end if -- (job done)
                rules[j] = rj
            end if
        end for 
    end for 
    for i=l to 1 by -1 do
        -- then substitute each backwards
        ri = rules[i]
        rii = ri[1]/ri[i+1] -- (all else should be 0)
        rules[i] = sprintf("%s = %d",{unknowns[i],rii})
        for j=i-1 to 1 by -1 do
            rj = rules[j]
            rji = rj[i+1]
            if rji!=0 then
                rules[j] = 0
                rj[1] -= rji*rii
                rj[i+1] = 0
                rules[j] = rj
            end if
        end for
    end for 
    res = join(rules,", ")
    printf(1,"%d: %v ==> %s\n",{n,sentences,res})
--  printf(1,"%d: %s\n",{n,res}) -- (maybe pref.)
    if res!=expected then ?9/0 end if
end procedure

printf(1,"\nStep 2: convert sentences into structures/equations, and solve them:\n")
for i=1 to count do
    sequence words = split(lines[i],{"."})
    sequence sentences = {},
             sentencii, -- (one ...but some still contain "and")
             unknowns = {}
    for w=1 to length(words) do
        {sentencii,unknowns} = parse_sentence(words[w],unknowns)
        sentences &= sentencii
    end for
    if length(sentences)>length(unknowns) then
        -- messy: puzzle has too much info!
        -- (14 aka "33 coins" and 17 "Terry" with 38 coins,
        --  eliminate wrongly and get a divide by zero...)
--      sentences = sentences[1..length(unknowns)]
        sentences[-2] = sentences[-1]
        sentences = sentences[1..length(unknowns)]
    end if
    if length(sentences)!=length(unknowns) then ?9/0 end if
    for s=1 to length(sentences) do
        -- pad any short equations, eg 3 more nickels than dimes
        -- needs a 0 for quarters, if were not mentioned before.
        sequence ss = sentences[s]
        integer padcode = ss[$]
        ss = ss[1..$-1]
        integer shortlen = length(sentences)+1-length(ss)
        if shortlen then
            switch padcode do
                case 0: ss &= repeat(0,shortlen)
                case 1: ss &= repeat(1,shortlen)
                case 'a':
                    for u=-shortlen to -1 do
                        string uu = unknowns[u]
                        integer k = find(uu,assets)
                        ss &= assetv[k]
                    end for
                default: ?9/0
            end switch
        end if
        sentences[s] = ss
    end for
    solveN(i,sentences,unknowns,expectations[i])
end for

integer k = find(false,vused)
if k then ?{"unused vocab",vocab[k]} end if
Output:

You just gotta love this Pidgin English! The problem numbering system used below is mine alone.
I was slightly unsure whether to interpolate these q&a outputs, but I think the separation chosen has its own merits.
The structures/equations of part 2 are completely unreadable at first, but quite simple really. 

24 puzzles:
Step 1: remove noise and otherwise simplify (if nothing else, down to a 31-word vocab):

1: 3 times asmany quarters as dimes . total money $5.95 . many quarters and dimes have?
2: 18 coins consisting pennies and nickels . total coins 38c . many pennies and nickels have?
3: 6 more quarters than nickels . total coins $3.00 . many nickels and quarters have?
4: 32 coins consisting nickels and quarters . total money $3.80 . many nickels and quarters have?
5: 2 times asmany dimes as pennies and 3 more nickels than pennies . total coins $1.97 . many each coin have?
6: 3 times asmany quarters as half_dollars and 6 more dimes than half_dollars . total money $4.65 . many each coin have?
7: $75 bills . 2 times asmany one_dollar_bills as five_dollar_bills and 1 less ten_dollar_bills than five_dollar_bills . many each bill have?
8: 8 coins consisting quarters and dimes . total $1.25 . many each coin have?
9: 3 times asmany dimes as nickels and 5 more pennies than nickels . total coins $1.13 . many each coin have?
10: 9 more dimes than nickels . total money $1.20 . many dimes have?
11: 20 bills consisting one_dollar_bills and two_dollar_bills . total money $35 . many two_dollar_bills have?
12: 8 more pennies than nickels and 3 more dimes than nickels . total money $3.10 . many dimes have?
13: 26 coins all dollars and quarters . total $17.00 . many each coin have?
14: 33 coins consisting nickels dimes and quarters . total $3.30 . 3 times asmany nickels as quarters and one-half asmany dimes as nickels . many coins each have?
15: same pennies nickels and dimes . coins total $1.44 . many each coin have?
16: 25 coins nickels and dimes . total $1.65 . many each coin have?
17: 2 more quarters than dimes . total $6.80 . quarters and dimes 38 . many quarters and dimes have?
18: one_dollar_bills five_dollar_bills and ten_dollar_bills . total $43 . 4 times asmany one_dollar_bills as ten_dollar_bills . total 13 bills . many each bill have?
19: 3 times asmany one_dollar_bills as five_dollar_bills . total $32 . many each bill have?
20: total $41.25 . 255 coins . only nickels dimes and quarters . 2 times asmany dimes as nickels . many each coin have?
21: 27 coins . total $4.50 . only quarters and dimes . many coins each have?
22: $13.25 nickels and quarters . 165 coins . many each coin have?
23: $45.25 quarters and dimes . 29 less quarters than dimes . many each coin have?
24: 12 coins consisting dimes and pennies . total money $0.30 . many each coin have?

Step 2: convert sentences into structures/equations, and solve them:
1: {{0,1,-3},{595,25,10}} ==> quarters = 21, dimes = 7
2: {{18,1,1},{38,1,5}} ==> pennies = 13, nickels = 5
3: {{6,1,-1},{300,25,5}} ==> quarters = 11, nickels = 5
4: {{32,1,1},{380,5,25}} ==> nickels = 21, quarters = 11
5: {{0,1,-2,0},{3,0,-1,1},{197,10,1,5}} ==> dimes = 14, pennies = 7, nickels = 10
6: {{0,1,-3,0},{6,0,-1,1},{465,25,50,10}} ==> quarters = 9, half_dollars = 3, dimes = 9
7: {{7500,100,500,1000},{0,1,-2,0},{1,0,1,-1}} ==> one_dollar_bills = 10, five_dollar_bills = 5, ten_dollar_bills = 4
8: {{8,1,1},{125,25,10}} ==> quarters = 3, dimes = 5
9: {{0,1,-3,0},{5,0,-1,1},{113,10,5,1}} ==> dimes = 9, nickels = 3, pennies = 8
10: {{9,1,-1},{120,10,5}} ==> dimes = 11, nickels = 2
11: {{20,1,1},{3500,100,200}} ==> one_dollar_bills = 5, two_dollar_bills = 15
12: {{8,1,-1,0},{3,0,-1,1},{310,1,5,10}} ==> pennies = 25, nickels = 17, dimes = 20
13: {{26,1,1},{1700,100,25}} ==> dollars = 14, quarters = 12
14: {{33,1,1,1},{330,5,10,25},{0,1,-2,0}} ==> nickels = 18, dimes = 9, quarters = 6
15: {{0,1,-1,0},{0,0,1,-1},{144,1,5,10}} ==> pennies = 9, nickels = 9, dimes = 9
16: {{25,1,1},{165,5,10}} ==> nickels = 17, dimes = 8
17: {{2,1,-1},{38,1,1}} ==> quarters = 20, dimes = 18
18: {{4300,100,500,1000},{0,1,0,-4},{13,1,1,1}} ==> one_dollar_bills = 8, five_dollar_bills = 3, ten_dollar_bills = 2
19: {{0,1,-3},{3200,100,500}} ==> one_dollar_bills = 12, five_dollar_bills = 4
20: {{4125,5,10,25},{255,1,1,1},{0,-2,1,0}} ==> nickels = 45, dimes = 90, quarters = 120
21: {{27,1,1},{450,25,10}} ==> quarters = 12, dimes = 15
22: {{1325,5,25},{165,1,1}} ==> nickels = 140, quarters = 25
23: {{4525,25,10},{29,-1,1}} ==> quarters = 121, dimes = 150
24: {{12,1,1},{30,10,1}} ==> dimes = 2, pennies = 10

Wren

Translation of: Go
Library: Wren-dynamic
Library: Wren-pattern
Library: Wren-str
Library: Wren-sort
Library: Wren-fmt
import "./dynamic" for Struct
import "./pattern" for Pattern
import "./str" for Str
import "./sort" for Sort
import "./fmt" for Fmt

var Kind = Struct.create("Kind", ["name", "value", "number"])

// variable1 = constant1 * variable2 + constant2
var Relation = Struct.create("Relation", ["variable1", "variable2", "constant1", "constant2"])

var nums = {
     "one-half": "0 times", "one": "1", "two": "2", "three": "3", "four": "4", "five": "5",
    "six": "6", "seven": "7", "eight": "8", "nine": "9", "ten": "10", "eleven": "11", "twelve": "12",
    "thirteen": "13", "fourteen": "14", "fifteen": "15", "sixteen": "16", "seventeen": "17",
    "eighteen": "18", "nineteen": "19", "twenty": "20", "thirty": "30", "forty": "40",
    "fifty": "50", "sixty": "60", "seventy": "70", "eighty": "80", "ninety": "90", "hundred": "100"
}

var nums2 = {
    "twenty-": "2", "thirty-": "3", "forty-": "4",
    "fifty-": "5", "sixty-": "6", "seventy-": "7", "eighty-": "8", "ninety-": "9"
}

var coins = {
    "pennies": 0.01, "nickels": 0.05, "dimes": 0.10, "quarters": 0.25, "half-dollars": 0.50,
    "one-dollar": 1.00, "two-dollar": 2.00, "five-dollar": 5.00, "ten-dollar": 10.00
}

var bills = {
    "$1": "one-dollar", "$2": "two-dollar", "$5": "five-dollar", "$10": "ten-dollar"
}

var rx1 = Pattern.new("[/$+1/f|+1/d¢]")
var rx2 = Pattern.new("[pennies|nickels|dimes|quarters|half-dollar|one-dollar|two-dollar|five-dollar|ten-dollar]")
var rx3 = Pattern.new("/s[+1/d]/s")
var rx4 = Pattern.new("[+1/d] times as many [+1/y] as [~she has |][+1/y]")
var rx5 = Pattern.new("[+1/d] more [+1/y] than [~she has |][+1/y]")
var rx6 = Pattern.new("[+1/d] less [+1/y] than [~she has |][+1/y]")
var rx7 = Pattern.new("[+1/d] dollars")

var spaced = Fn.new { |s| " %(s) " }

// Gets a sorted list of monetary values.
var getValues = Fn.new { |q|
    var ss = rx1.findAll(q).map { |m| m.text.trimEnd(".") }.toList
    if (ss.count == 0) return []
    var res = []
    for (s in ss) {
        if (s == "") continue
        if (s[0] == "$") {
            s = s[1..-1]
        } else {
            s = "." + s[0..-3] // '¢' is 2 bytes
        }
        var f = Num.fromString(s)
        res.add(f)
    }
    res.sort()
    return res
}

// Gets a sorted slice of non-monetary integers.
var getNumbers = Fn.new { |q|
    var ns = rx3.findAll(q).map { |m| m.text }.toList
    if (ns.count == 0) return null
    var res = []
    for (n in ns) {
        var i = Num.fromString(n)
        res.add(i)
    }
    res.sort()
    return res
}

// Gets the 'kinds' for the problem.
var getKinds = Fn.new { |a|
    var num = Num.fromString(a[1])
    var kinds = [Kind.new(a[2], 0, 0), Kind.new(a[4], 0, 0)]
    var areCoins = false
    for (i in 0...kinds.count) {
        var v = coins[kinds[i].name]
        if (v) {
            kinds[i].value = v
            areCoins = true
        }
    }
    if (!areCoins) return [0, null]
    return [num, kinds]
}

// Checks if the problem involves 3 coins and
// also returns their names and the names of the coins which occur most.
var hasThreeCoins = Fn.new { |q|
    q = q.replace(".", "").replace(",", "")
    var words = q.split(" ")
    var coinMap = {}
    for (word in words) {
        if (coins.containsKey(word)) {
            var v = coinMap[word]
            if (v) {
                coinMap[word] = v + 1
            } else {
                coinMap[word] = 1
            }
        }
    }
    if (coinMap.count != 3) return [null, "", false]
    var maxNum = 0
    var maxNames = []
    var names = []
    for (me in coinMap) {
        names.add(me.key)
        if (me.value > maxNum) {
            maxNum = me.value
            maxNames = [me.key]
        } else if (me.value == maxNum) {
            maxNames.add(me.key)
        }
    }
    return [names, maxNames, true]
}

var errorMsg = Fn.new { |p|
    System.print(p)
    System.print("*** CAN'T SOLVE THIS ONE ***\n")
}

var printAnswers = Fn.new { |p, kinds|
    System.print(p)
    System.write("ANSWER:")
    var i = 0
    for (kind in kinds) {
        if (i > 0) System.write(",")
        System.write(" %(kind.number) %(kind.name)")
        i = i + 1
    }
    System.print("\n")
}

// Processes a problem which involves 3 coins.
var threeCoins = Fn.new { |p, q, names, maxNames|
    var relations = []
    var am = rx4.findAll(q).map { |m| [m.text] + m.capsText }.toList
    for (i in 0...am.count) {
        var res = getKinds.call(am[i])
        var mult = res[0]
        var kinds = res[1]
        relations.add(Relation.new(kinds[0].name, kinds[1].name, mult, 0))
    }
    var mt = rx5.findAll(q).map { |m| [m.text] + m.capsText }.toList
    for (i in 0...mt.count) {
        var res = getKinds.call(mt[i])
        var plus = res[0]
        var kinds = res[1]
        relations.add(Relation.new(kinds[0].name, kinds[1].name, 1, plus))
    }
    var lt = rx6.findAll(q).map { |m| [m.text] + m.capsText }.toList
    for (i in 0...lt.count) {
        var res = getKinds.call(lt[i])
        var minus = res[0]
        var kinds = res[1]
        relations.add(Relation.new(kinds[0].name, kinds[1].name, 1, -minus))
    }
    var le = relations.count
    if (le > 2) {
        errorMsg.call(p)
        return
    }
    if (le == 0) { // numbers of each coin must be the same
        var sum = 0
        for (name in names) sum = sum + coins[name]
        var tv = getValues.call(q)[-1]
        var n = (tv/sum + 0.5).floor
        var kinds = []
        for (name in names) kinds.add(Kind.new(name, 0, n))
        printAnswers.call(p, kinds)
    } else {
        var totalValue = getValues.call(q)[-1]
        for (maxName in maxNames) {
            for (i in 0...le) {
                if (relations[i].constant1 == 0) {
                    relations[i].constant1 = 0.5 // deals with 'one-half' cases
                }
                if (le == 2 && maxName == relations[i].variable1) {
                    var v = relations[i].variable2
                    relations[i].variable1 = v
                    relations[i].variable2 = maxName
                    relations[i].constant1 = 1 / relations[i].constant1
                    relations[i].constant2 = -relations[i].constant2
                }
            }
            var tv = totalValue
            var v1 = ""
            var v2 = ""
            var v3 = ""
            var n1 = 0
            var n2 = 0
            var n3 = 0
            if (le == 2) {
                var tmc = coins[relations[0].variable1] * relations[0].constant1 +
                    coins[relations[1].variable1] * relations[1].constant1 + coins[maxName]
                tv = tv - coins[relations[0].variable1] * relations[0].constant2 -
                    coins[relations[1].variable1] * relations[1].constant2
                v1 = maxName
                v2 = relations[0].variable1
                v3 = relations[1].variable1
                n1 = (tv/tmc + 0.5).floor
                n2 = (relations[0].constant1*n1 + relations[0].constant2 + 0.5).floor
                n3 = (relations[1].constant1*n1 + relations[1].constant2 + 0.5).floor
            } else {
                var tn = getNumbers.call(q)[-1]
                v1 = relations[0].variable1
                v2 = relations[0].variable2
                for (name in names) {
                    if (name != v1 && name != v2) {
                        v3 = name
                        break
                    }
                }
                var mult1 = coins[v1]
                var mult2 = coins[v2]
                var mult3 = coins[v3]
                n2 = (((tn-relations[0].constant2)*mult3-tv+relations[0].constant2*mult1)/
                    ((relations[0].constant1+1)*mult3-relations[0].constant1*mult1-mult2) + 0.5).floor
                n1 = (n2*relations[0].constant1 + relations[0].constant2 + 0.5).floor
                n3 = tn.floor - n1 - n2
            }
            var calcValue = n1 * coins[v1] + n2 * coins[v2] + n3 * coins[v3]
            if ((totalValue - calcValue).abs <= 1e-14) {
                var kinds = [Kind.new(v1, 0, n1), Kind.new(v2, 0, n2), Kind.new(v3, 0, n3)]
                printAnswers.call(p, kinds)
                return
            }
        }
        errorMsg.call(p)
    }
}

var ps = [
    "If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.",
    "A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.",
    "A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.",
    "A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.",
    "A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.",
    "In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.",
    "A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.",
    "A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.",
    "An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?",
    "A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?",
    "A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?",
    "A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?",
    "A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.",
    "A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.",
    "A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.",
    "A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.",
    "Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?",
    "A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?",
    "A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?",
    "Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?",
    "Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?",
    "In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?",
    "Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?",
    "A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?",
    "Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?",
    "Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?",
    "Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?",
    "A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?"
]
for (p in ps) {
    var q = Str.lower(p).replace("twice", "two times").replace(" does ", " has ")
    for (d in ["half", "one", "two", "five", "ten"]) {
        q = q.replace(d + " dollar", d + "-dollar")
    }
    for (me in nums) {
        q = q.replace(spaced.call(me.key), spaced.call(me.value))
    }
    for (me in nums2) {
        q = q.replace(me.key, me.value)
    }
    for (me in nums) {
        q = q.replace(me.key + " ", me.value + " ")
    }
    for (me in bills) {
        q = q.replace(me.key + " ", me.value + " ")
    }
    q = q.replace(" bills", "").replace(" bill", "")
    // check if there are 3 coins involved
    var res = hasThreeCoins.call(q)
    if (res[2]){
        threeCoins.call(p, q, res[0], res[1])
        continue
    }
    var am = rx4.findAll(q).map { |m| [m.text] + m.capsText }.toList
    if (am.count == 1) {
        var res = getKinds.call(am[0])
        var mult = res[0]
        var kinds = res[1]
        if (!kinds) {
            errorMsg.call(p)
            continue
        }
        var tv = getValues.call(q)[-1]
        kinds[1].number = (tv/(mult*kinds[0].value + kinds[1].value) + 0.5).floor
        kinds[0].number = kinds[1].number * mult
        printAnswers.call(p, kinds)
        continue
    }
    var mt = rx5.findAll(q).map { |m| [m.text] + m.capsText }.toList
    if (mt.count == 1) {
        var res = getKinds.call(mt[0])
        var plus = res[0]
        var kinds = res[1]
        if (!kinds) {
            errorMsg.call(p)
            continue
        }
        var tv = getValues.call(q)[-1]
        kinds[1].number = ((tv-plus*kinds[0].value)/(kinds[0].value + kinds[1].value) + 0.5).floor
        kinds[0].number = kinds[1].number + plus
        printAnswers.call(p, kinds)
        continue
    }
    var lt = rx6.findAll(q).map { |m| [m.text] + m.capsText }.toList
    if (lt.count == 1) {
        var res = getKinds.call(lt[0])
        var minus = res[0]
        var kinds = res[1]
        if (!kinds) {
            errorMsg.call(p)
            continue
        }
        var tv = getValues.call(q)[-1]
        kinds[1].number = ((tv+minus*kinds[0].value)/(kinds[0].value + kinds[1].value) + 0.5).floor
        kinds[0].number = kinds[1].number - minus
        printAnswers.call(p, kinds)
        continue
    }
    res = getValues.call(q)
    var tv = 0
    if (res.count > 0) {
        tv = res[-1]
    } else {
        var res3 = rx7.findAll(q).map { |m| [m.text] + m.capsText }.toList
        tv = Num.fromString(res3[0][1])
    }
    var tn = getNumbers.call(q)[-1]
    var coinNames = rx2.findAll(q).map { |m| m.text }.toList
    Sort.insertion(coinNames)
    var kinds = []
    if (coinNames.count > 0) {
        kinds.add(Kind.new(coinNames[0], coins[coinNames[0]], 0))
        for (i in 1...coinNames.count) {
            if (coinNames[i] != coinNames[i-1]) {
                kinds.add(Kind.new(coinNames[i], coins[coinNames[i]], 0))
            }
        }
        if (kinds.count != 2) {
            errorMsg.call(p)
            continue
        }
    } else if (res.count >= 3) {
        kinds.add(Kind.new(Fmt.swrite("$$$.2f item", res[0]), res[0], 0))
        for (i in 1...res.count-1) {
            if (res[i] != res[i-1]) {
                kinds.add(Kind.new(Fmt.swrite("$$$.2f item", res[i]), res[i], 0))
            }
        }
        if (kinds.count!= 2) {
            errorMsg.call(p)
            continue
        }
    } else {
        errorMsg.call(p)
        continue
    }
    kinds[0].number = ((tv-tn*kinds[1].value)/(kinds[0].value-kinds[1].value) + 0.5).floor
    kinds[1].number = tn - kinds[0].number
    printAnswers.call(p, kinds)
}
Output:
If a person has three times as many quarters as dimes and the total amount of money is $5.95, find the number of quarters and dimes.
ANSWER: 21 quarters, 7 dimes

A pile of 18 coins consists of pennies and nickels. If the total amount of the coins is 38¢, find the number of pennies and nickels.
ANSWER: 5 nickels, 13 pennies

A small child has 6 more quarters than nickels. If the total amount of coins is $3.00, find the number of nickels and quarters the child has.
ANSWER: 11 quarters, 5 nickels

A child's bank contains 32 coins consisting of nickels and quarters. If the total amount of money is $3.80, find the number of nickels and quarters in the bank.
ANSWER: 21 nickels, 11 quarters

A person has twice as many dimes as she has pennies and three more nickels than pennies. If the total amount of the coins is $1.97, find the numbers of each type of coin the person has.
ANSWER: 7 pennies, 14 dimes, 10 nickels

In a bank, there are three times as many quarters as half dollars and 6 more dimes than half dollars. If the total amount of the money in the bank is $4.65, find the number of each type of coin in the bank.
ANSWER: 3 half-dollars, 9 quarters, 9 dimes

A person bought 12 stamps consisting of 37¢ stamps and 23¢ stamps. If the cost of the stamps is $3.74, find the number of each type of the stamps purchased.
ANSWER: 5 $0.23 item, 7 $0.37 item

A dairy store sold a total of 80 ice cream sandwiches and ice cream bars. If the sandwiches cost $0.69 each and the bars cost $0.75 each and the store made $58.08, find the number of each sold.
ANSWER: 32 $0.69 item, 48 $0.75 item

An office supply store sells college-ruled notebook paper for $1.59 a ream and wide-ruled notebook paper for $2.29 a ream. If a student purchased 9 reams of notebook paper and paid $15.71, how many reams of each type of paper did the student purchase?
ANSWER: 7 $1.59 item, 2 $2.29 item

A clerk is given $75 in bills to put in a cash drawer at the start of a workday. There are twice as many $1 bills as $5 bills and one less $10 bill than $5 bills. How many of each type of bill are there?
ANSWER: 5 five-dollar, 10 one-dollar, 4 ten-dollar

A person has 8 coins consisting of quarters and dimes. If the total amount of this change is $1.25, how many of each kind of coin are there?
ANSWER: 5 dimes, 3 quarters

A person has 3 times as many dimes as he has nickels and 5 more pennies than nickels. If the total amount of these coins is $1.13, how many of each kind of coin does he have?
ANSWER: 3 nickels, 9 dimes, 8 pennies

A person bought ten greeting cards consisting of birthday cards costing $1.50 each and anniversary cards costing $2.00 each. If the total cost of the cards was $17.00, find the number of each kind of card the person bought.
ANSWER: 6 $1.50 item, 4 $2.00 item

A person has 9 more dimes than nickels. If the total amount of money is $1.20, find the number of dimes the person has.
ANSWER: 11 dimes, 2 nickels

A person has 20 bills consisting of $1 bills and $2 bills. If the total amount of money the person has is $35, find the number of $2 bills the person has.
ANSWER: 5 one-dollar, 15 two-dollar

A bank contains 8 more pennies than nickels and 3 more dimes than nickels. If the total amount of money in the bank is $3.10, find the number of dimes in the bank.
ANSWER: 17 nickels, 25 pennies, 20 dimes

Your uncle walks in, jingling the coins in his pocket. He grins at you and tells you that you can have all the coins if you can figure out how many of each kind of coin he is carrying. You're not too interested until he tells you that he's been collecting those gold-tone one-dollar coins. The twenty-six coins in his pocket are all dollars and quarters, and they add up to seventeen dollars in value. How many of each coin does he have?
ANSWER: 14 one-dollar, 12 quarters

A collection of 33 coins, consisting of nickels, dimes, and quarters, has a value of $3.30. If there are three times as many nickels as quarters, and one-half as many dimes as nickels, how many coins of each kind are there?
ANSWER: 18 nickels, 6 quarters, 9 dimes

A wallet contains the same number of pennies, nickels, and dimes. The coins total $1.44. How many of each type of coin does the wallet contain?
ANSWER: 9 pennies, 9 dimes, 9 nickels

Suppose Ken has 25 coins in nickels and dimes only and has a total of $1.65. How many of each coin does he have?
ANSWER: 8 dimes, 17 nickels

Terry has 2 more quarters than dimes and has a total of $6.80. The number of quarters and dimes is 38. How many quarters and dimes does Terry have?
ANSWER: 20 quarters, 18 dimes

In my wallet, I have one-dollar bills, five-dollar bills, and ten-dollar bills. The total amount in my wallet is $43. I have four times as many one-dollar bills as ten-dollar bills. All together, there are 13 bills in my wallet. How many of each bill do I have?
ANSWER: 8 one-dollar, 2 ten-dollar, 3 five-dollar

Marsha has three times as many one-dollar bills as she does five dollar bills. She has a total of $32. How many of each bill does she have?
ANSWER: 12 one-dollar, 4 five-dollar

A vending machine has $41.25 in it. There are 255 coins total and the machine only accepts nickels, dimes and quarters. There are twice as many dimes as nickels. How many of each coin are in the machine?
ANSWER: 90 dimes, 45 nickels, 120 quarters

Michael had 27 coins in all, valuing $4.50. If he had only quarters and dimes, how many coins of each kind did he have?
ANSWER: 15 dimes, 12 quarters

Lucille had $13.25 in nickels and quarters. If she had 165 coins in all, how many of each type of coin did she have?
ANSWER: 140 nickels, 25 quarters

Ben has $45.25 in quarters and dimes. If he has 29 less quarters than dimes, how many of each type of coin does he have?
ANSWER: 121 quarters, 150 dimes

A person has 12 coins consisting of dimes and pennies. If the total amount of money is $0.30, how many of each coin are there?
ANSWER: 2 dimes, 10 pennies
Retrieved from "https://rosettacode.org/wiki/Solving_coin_problems?oldid=352152"