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16 August, 17:40

A pile of coins, consisting of quarters and half dollars, is worth $11.75. If there are 2 more quarters than half dollars, how many of each are there?

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  1. 16 August, 19:43
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    The pile contains 17 quarters and 15 half-dollars.

    Let x = the number of quarters and y = the number of half-dollars.

    We have two equations:

    (1) $0.25x + $0.50y = $11.75

    (2) x = y + 2

    Substitute the value of x from Equation (2) into Equation (1).

    0.25 (y+2) + 0.50y = 11.75

    0.25y + 0.50 + 0.50y = 11.75

    0.75y = 11.75 - 0.50 = 11.25

    y = 11.25/0.75 = 15

    Substitute the value of y in Equation (2).

    x = 15 + 2 = 17

    The pile contains 17 quarters and 15 half-dollars.

    Check: 17*$0.25 + 15*$0.50 = $4.25 + $7.50 = $11.75.
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