Acollection of 102 nickels, dimes, and quarters is worth $13.60. there are 14 more nickels than dimes. how many quarters are there?

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

                                                                                             Q = 36

36 quarters