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11 May, 11:55

How many different ways can you make 50 cents if you have 1 quarter, 5 dimes, and 10 nickels?

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  1. 11 May, 12:19
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    Answer: There are 10 different ways!

    Explanation:

    You need to find non-negative numbers N, D, and Q so that:

    5N + 10D + 25Q = 50

    N + 2D + 5Q = 10

    Q = 0, 1, 2

    If Q = 1, then you have:

    N + 2D = 5

    Q = 1, D = 2, N = 1

    Q = 1, D = 1, N = 3

    Q = 1, D = 0, N = 5

    N + 2D = 10

    This gives the last solutions:

    Q = 0, D = 5, N = 0

    Q = 0, D = 4, N = 2

    Q = 0, D = 3, N = 4

    Q = 0, D = 2, N = 6

    Q = 0, D = 1, N = 8

    Q = 0, D = 0, N = 10
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