assuming the largest coin denomintion is a quarter.
let there be n quarters,
then 2n dimes
4n nickels and
x pennies
25n + 10(2n) + 5(4n) + x = 100
65n + x = 100
x = 100 - 65n
n can only be 1, if n = 2 or more, you have a negative x
so 1 quarter, 2 dimes, 4 nickels and 35 pennies.
another solution would be:
quarters - n
nickels - 2n
dimes - 4n
pennies - x
25n + 5(2n) + 10(4n) + x = 100
75n + x = 100
again n can only be 1, and x = 25
so
1 quarter
2 nickels
4 dimes
25 pennies
you could also make up a combination of half-dollar, dimes, nickels and pennies
Make a combination that's worth one dollar where you have one of sum kind of coin, doulbe of another, double that of another, and some number of the last coin
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