Roman C. answered • 09/11/15

Masters of Education Graduate with Mathematics Expertise

Let N be the number of nickels, D be the number of dimes, and Q be the number of quarters.

In order of the clues, the three equations are:

(1): 0.05N + 0.10D + 0.25Q = 6.30

(2): Q = D + 9

(3): N = 5Q

Plug in (2) into (3) to get

(4): N = 5(D + 9)

Plug (2) and (4) into (1)

0.05·5(D + 9) + 0.10D + 0.25(D + 9) = 6.30

0.50(D + 9) + 0.10D = 6.30

0.50D + 4.50 + 0.10D = 6.30

0.60D + 4.50 = 6.30

0.60 D = 1.80

D = 1.80/0.60 = 3

Back substitute.

Q = D + 9 = 3 + 9 = 12

N = 5Q = 5·12 = 60

So the carrier has 60 nickels, 3 dimes, and 12 quarters.