Answer:
7 nickels
20 dimes
5 quarters
Explanation:
n=nickels. d=dimes. q=quarters
n+d+q=32
0.05n+0.1d+0.25q=3.60
d=8+n+q
Solve for number of dimes:
d-8=8-8+n+q
d-8=n+q
d-d-8=n+q-d
-8=n+q-d
32=n+q+d
- (-8=n+q-d)
32 - (-8) = n-n + q-q + d-(-d)
32 + 8 = d + d
40 = 2d
d = 20 => simplify
20=8+n+q ==> substitute 20 for d (d=8+n+q)
20-8 = 8-8+n+q
n+q = 12
0.05n+0.1(20)+0.25q=3.60 ==> substitute 20 for d
0.05n + 2 + 0.25q = 3.60
(0.05n + 2 + 0.25q = 3.60)*100 ->remove the decimals by multiplying by 100
5n + 200 + 25q = 360
5n + 200 - 200 + 25q = 360 - 200
5n + 25q = 160
Solve for number of quarters:
(5n + 25q)/5 = 160/5 ==> simplify the equation
n + 5q = 32
- (n + q = 12)
n-n + 5q-q = 32-12
0 + 4q = 20
4q = 20
q = 5 ==> simplify
Solve for number of nickels:
n+20+5=32 ==> plug in 20 for d and 5 for q (n+d+q=32)
n+25=32
n+25-25=32-25 ==> solve for n
n=7 ==> simplify
n=7: 7 nickels
d = 20: 20 dimes
q = 5: 5 quarters