Question

A vending machines coin box contains nickels dimes and quarters the total number of coins in the box is 312 the number of dimes is three times the number of nickels and quarters together and the box contains $31.30 find the number of nickels dimes and quarters that it contains

Answer 1

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