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Math Help - Money problem

  1. #1
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    Smile Money problem

    Ann gaev Betty as many cents as Betty had. Betty then gave Ann as many cents as Ann then had.At this point, each had 12 cents. How many did Ann have at the beginning?

    We actually have tried to work this out with pennies going back and forth betweent he 2 of us, but can't figure it out. Any help wuold be appreciated!
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  2. #2
    Super Member Aryth's Avatar
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    Let's go forward and then backward on this problem.

    Ann gave Betty as many cents as Betty had.

    Ann gave Betty what she already had, which means that you have:

    What Betty has now = What Betty already had + What Ann gave Betty

    But this is:

    What Betty has now = What Betty already had + What Betty already had

    What Betty has now = 2*What Betty already had

    Now, we look at the next statement:

    Betty then gave Ann as many cents as Ann already had

    Now, we need to find out what she has:

    What Ann has now = What Ann already had + What Betty gave Ann

    What Ann has now = What Ann already had + What Ann already had

    What Ann has now = 2*(What Ann already had)

    But now Betty has less cents than before because she gave Ann what Ann already had:

    What Betty has now = 2*(What Betty already had) - What Ann already had

    So, at this point they both have 12 cents, which means:

    What Ann has now = 2*(What Ann already had) = 12

    This give you:

    (Ann already had) = 6 cents

    Now, you know:

    What Betty has now = 2*(What Betty already had) - What Ann already had = 12

    2*(What Betty already had) - 6 = 12

    2*(What Betty already had) = 18

    What Betty already had = 9 cents

    And there you go, you can work through it to make sure.

    Ann starts with 6 cents, Betty with 9

    Ann gives betty what betty already has, 9 + 9 = 18

    Betty gives ann what ann already has, 6 + 6 = 12, 18 - 6 = 12

    And there you go. This is a slightly harder problem than I expected though.
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