A pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarte

Discussion in 'Calculator Requests' started by math_celebrity, Oct 29, 2016.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    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?

    Let h be the number of half-dollars and q be the number of quarters. Set up two equations:
    (1) q = h + 2
    (2) 0.25q + 0.5h = 11.75

    Substitute (1) into (2)
    0.25(h + 2) + 0.5h = 11.75
    0.25h + 0.5 + 0.5h = 11.75

    Group h terms
    0.75h + 0.5 = 11.75

    Subtract 0.5 from each side
    0.75h = 11.25

    Divide each side by h
    h = 15

    Substitute h = 15 into (1)
    q = 15 + 2
    q = 17
     

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