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24 April, 18:06

A store is selling two mixtures of coffee beans in one-pound bags. The first mixture has 12 ounces of Sumatra combined with 44 ounces of Celebes Kalossi, and costs $42. The second mixture has 44 ounces of Sumatra and 12ounces of Celebes Kalossi, and costs $30. How much does one ounce of Sumatra and one ounce of Celebes Kalossi cost?

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  1. 24 April, 18:29
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    Create 2 equations for the given problem

    12s + 44c = 42

    44s + 12c = 30

    Take either equation and solve for either s or c.

    12s + 44c = 42

    12s = 42 - 44c

    s = (42 - 44c) / 12

    s = (21 - 22c) / 6

    Substitute into 2nd equation

    44s + 12c = 30

    22 ((21 - 22c) / 3) + 12c = 30

    22 (21 - 22c) + 36c = 90

    -448c + 462 = 90

    -448c = - 372

    c = - 372/-448

    c = 93/112

    c = 0.83

    Substitute into the 2nd equation

    44s + 12c = 30

    44s = 30 - 12c

    s = (30 - 12 (93/112)) / 44

    s = (30 - 279 / 28) / 44)

    s = (30 - 9 27/28) / 44

    s = 0.46

    Prove

    12s + 44c = 42

    12 (0.46) + 44 (0.83) = 42

    5.52 + 36.52 = 42

    42.04 = 42

    44s + 12c = 30

    44 (0.46) + 12 (0.83) = 30

    20.24 + 9.96 = 30.16

    Assuming minor rounding issues this looks accurate.
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