Answer:
Explanation:
n = nickels
d = dimes
q = quarters
 
1) n + d + q = 39
 
n+d = q - 3
 
Translate to: 2) n + d - q = -3
 
.05n + .1d + .25q = 6.7 amount of each coin times the number of coins must add to 6.7
Multiply both sides by 20...
 
3) 1n + 2d + 5q = 134
 
 
Combine 1) & 2)
n + d + q = 39
n + d - q = -3
 
Add together
 
2n + 2d = 36
 
Divide by 2:
 
4) n + d = 18
 
 
Combine 1) and 3)
 
n + d + q = 39 Multiply by -5 => -5n -5d -5q = -195
n + 2d + 5q = 134 n + 2d + 5q = 134
 
Add together-> 5) -4n - 3d = -61
 
 
Combine 4) and 5)
 
 n + d = 18 Multiply by 4 => 4n + 4d = 72
-4n - 3d = 61 -4n - 3d = -61
 
Add: d = 11
 
11 dimes...
 
Plug that into 4)
 
n + 11 = 18
 
n = 18-11 = 7 nickels.
 
Plug that into 1.
 
n + d + q = 39
 
7 + 11 + q = 39
18 + q = 39
 
q = 39-18 = 21 quarters
 
21 quarters, 7 nickels, and 11 dimes.
 
21(.25) + 7(.05) + 11(.1) = 5.25 + .35 + 1.1 = 5.6 + 1.1 = 6.7 Check.