Ask Question
8 January, 15:00

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.

+2
Answers (1)
  1. 8 January, 18:45
    0
    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
Know the Answer?
Not Sure About the Answer?
Get an answer to your question ✅ “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 ...” in 📙 Business if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers