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10 January, 09:56

I have 8 pennies and some quarters, nickels, and dimes. The number of pennies plus nickels equals the number of dimes. I have 3 quarters for every 2 pennies and 3 dimes for every 2 quarters. How many coins are nickels?

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  1. 10 January, 10:54
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    There are five nickels.

    Let w = the number of pennies; x = the number of nickels; y = the number of dimes; z = the number of quarters.

    Then, we have three equations with four unknowns:

    (1) w + x = y

    (2) 3w = 2z

    (3) 2y = 3z

    However, there is a fourth unstated condition: w, x, y, and z must all be integers.

    Assume that z = 6 (to avoid fractions).

    From Equation (2), w = 4.

    From Equation (3), y = 9.

    Insert the values for w and y into equation (1).

    4 + x = 9

    x = 9 - 4 = 5

    Thus, there are 4 pennies, 5 nickels, 9 dimes, and 6 quarters.

    Check: 4 pennies + 5 nickels = 9 dimes

    6 quarters + 4 pennies = 3 quarters for every 2 pennies

    9 dimes + 6 quarters = 3 dimes for every 2 quarters
  2. 10 January, 11:17
    0
    Answer:8 pennies, 12 quarters, 18 dimes, so there are 10 nickels
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