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15 February, 21:51

Team Alpha had one fourth as many people as team Beta. After 6 people quit team Beta and 12 people were transferred to team Alpha from team Beta, both teams became equal. How many people were there originally on team Alpha?

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  1. 15 February, 22:07
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    Let "a" and "b" represent the numbers of people on teams Alpha and Beta, respectively. The problem statement tells you

    a = (1/4) b

    b - 6 - 12 = a + 12

    The first equation can be rewritten to give an expresion for b:

    b = 4a

    This can be substituted into the second equation to get

    4a - 18 = a + 12

    3a = 30

    a = 10

    There were originally 10 people on team Alpha.
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