A vending machine's coin box contains nickels, dimes, and quarters. The total number of coins in the box is 284. The number of dimes is three times the number of nickels and quarters together. If the box contains 27 dollars and 25 cents, find the number of nickels, dimes and quarters that it contains.

there are 59 nickels, 12 quarters, and 213 dimes

Explanation:

let n = nickels let q = quarters let d = dimes

first step:

d = 3 (n + q) = 3n + 3q

d + n + q = 284

0.10d + 0.05n + 0.25q = 27.25

second step:

3n + 3q + n + q = 284

0.10 (3n + 3q) + 0.5n + 0.25q = 27.25

third step:

4n + 4q = 284

0.3n + 0.3q + 0.05n + 0.25q = 27.25

fourth step:

n + q = 71

0.35n + 0.55q = 27.25

fifth step:

replace q = 71 - n

0.35n + 0.55 (71 - n) = 27.25

sixth step:

0.35n + 39.05 - 0.55n = 27.25

seventh step:

11.8 = 0.2n

eighth step:

n = 59

q = 71 - 59 = 12

d = 284 - n - q = 284 - 59 - 12 = 213