Answer:
58 nickels; 234 dimes; 20 quarters
Explanation:
number of dimes = d
number of nickels = n
number of quarters = q
n + d + q = 312
d = 3(n + q)
0.05n + 0.1d + 0.25q = 31.3
n + d + q = 312
d = 3n + 3q
5n + 10d + 25q = 3130
n + 3n + 3q + q = 312
5n + 30n + 30q + 25q = 3130
4n + 4q = 312
35n + 55q = 3130
n + q = 78
7n + 11q = 626
n = 78 - q
7(78 - q) + 11q = 626
546 - 7q + 11q = 626
4q = 80
q = 20
n = 78 - 20 = 58
d = 3(58 + 20) = 3(78) = 234
Answer: 58 nickels; 234 dimes; 20 quarters