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In a basketball game Maria scored 3 times as many points as Holly. In the next game, Maria scored 7 fewer points than she did in the first game, while Holly scored 9 more points than she did in the first game. If they scored the same number of points in the second game, how many points did each score in the first.

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  1. m1 = 3h1
    m2 = m1-7
    h2 = h1+9
    m2 = h2
    now make some substitutions looking for m1 and h1

    m1 = 3(h2-9) = 3(m2-9) = 3(m1-7-9)
    m1 = 3m1 - 48
    2m1 = 48
    m1 = 24
    so, h1 = 8

    check: m2 = 24-7 = 17 = 8+9 = h2

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