Question

Ben has a collection of quarters and nickels worth $5.35. If the number of nickels is five less than twice the number of quarters, find the number of each coin.


24 Quarters and 2 Nickels


6 Quarters and 51 Nickels


12 Quarters and 15 Nickels


16 Quarters and 27 Nickels

Answer 1

Let q = number of quarters and n = number of nickels.

We have 25q + 5n = 535 and n = 2q − 5. Substitute:
25q + 5(2q − 5) = 535
25q + 10q − 25 = 535
35q = 560 → q = 16
n = 2(16) − 5 = 27

So there are 16 quarters and 27 nickels (the fourth choice).