Question
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
Answers
Reiny
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
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