Question

A collection of 102 nickels, dimes, and quarters is worth $13.60. There are 14 more nickels than dimes. How many quarters are there?

Answer 1

nickels ($0.05): D + 14

dimes ($0.10): D

quarters ($0.25): Q

Quantity: (D + 14) + D + Q = 102 ⇒ 2D + 14 + Q = 102 ⇒ 2D + Q = 88

Value: 0.05(D + 14) + 0.10(D) + 0.25(Q) = 13.60 ⇒ 0.05D + 0.70 + 0.10D + 0.25Q = 13.60 ⇒ 0.15D + 0.70 + 0.25Q = 13.60 ⇒ 0.15D + 0.25Q = 12.90 ⇒ 15D + 25Q = 1290

2D + Q = 88 ⇒ -15(2D + Q = 88) ⇒ -30D - 15Q = -1320

15D + 25Q = 1290 ⇒ 2(15D + 25Q = 1290) ⇒ 30D + 50Q = 2580

35Q = 1260

`(35Q)/(35) = (1260)/(35)`

Q = 36

Answer: 36 quarters