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Math Help - Algebra?

  1. #1
    Junior Member
    Joined
    May 2009
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    68

    Unhappy Algebra?

    So I was given an assignment with 50 questions.
    And I dont know how to do this one:

    One evening, Andy, Barb and Carol play three rounds of a betting game with the understanding that the person who comes last in each round must double the money of the other two. After thrree rounds, each person has been last just once and each has $24. The amount that Andy started with at the beginning of the evening could have been:
    (A) 36 (B) 37 (C) 38 (D) 39 (E) 40

    And could you explain why?
    Thanks ^_^
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  2. #2
    Super Member malaygoel's Avatar
    Joined
    May 2006
    From
    India
    Posts
    648
    Since, much is not given here I assume that the full amount of the players is doubled.

    After the end of three rounds, amounts of the players were(in dollars)
    24,24,24

    Let us say that the third player lost the third round. Hence, the amount the players possess at the beginning of third round(and at the end of second round)

    12,12,48

    Let us say that the second player lost the second round. Hence, the amount the players possess at the beginning of second round(and at the end of first round)

    6,42,24

    Let us say that the first player lost the first round. Hence, the amount the players possess at the beginning of first round(and at the end of first round)

    39,21,12
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