1/3as many dimes as nickels. 3 more quarters than nickels 17 coins in all

You will set this up as follows, with nickels being the "base"

1/3n = dimes
n = nickels
n+3 = quarters

1/3n + n + n + 3 = 17
(2 1/3n) + 3 = 17
(2 1/3n) = 14
7/3n = 14
3/7 * 7/3n = 14 * 3/7
n = 6

6 nickels (n)
2 dimes (1/3n)
9 quarters (n+3)