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Math Help - pre-algebra problem

  1. #1
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    pre-algebra problem

    Tina, Dawn & Harry have $175 together. Tina has 3x as much as Dawn. Dawn has 2x as much money as Harry. How much money does each have?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by splits1 View Post
    Tina, Dawn & Harry have $175 together. Tina has 3x as much as Dawn. Dawn has 2x as much money as Harry. How much money does each have?
    Let T,\,D,\,H represent the amount of money Tina, Dawn, and Harry have respectively.

    So we know that

    T+D+H=175 -- (1)

    T=3D -- (2)

    D=2H -- (3)

    Subbing (3) into (2), we can see that

    T=6H -- (4)

    Now substitute (4) and (3) into (1) to get

    6H+2H+H=175\implies 9H=175\implies H=19.44

    Thus, T=6(19.44)=116.64 and D=2(19.44)=38.88

    (Note that when we go to check our answer, we have 19.44+38.88+116.64=174.96\approx175 due to rounding errors.)

    Does this make sense?
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  3. #3
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    Are you sure you have copied the problem exactly? Although I can solve this, the end result does not divide evenly. If they had 175.50 together, then each would have an evenly dividable amount.

    But, going with what you wrote:

    Let x = Harry's money
    2x = Dawn's money (since Dawn has 2 times as much money as Harry)
    3(2x) = Tina's money (Tina has 3 times as much as Dawn)

    All together they have $175.

    x + 2x + 3(2x) = 175

    Collect like terms on the LHS, then divide both sides by the coefficient of x. That will solve for x, which is Harry's money. Then multiply x by the right amounts to calculate Dawn and Tina's money.
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  4. #4
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    Yes, it makes sense. Thank you very much!!
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