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Math Help - Need Help

  1. #1
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    Need Help

    Can somebody please help with this challenging question?

    m sweets are shared among Amanda, Beatrice and Christina. Beatrice has h/2 times as many sweets as Christina while Amanda's share is g times of Beatrice's share.
    a) express and simplify, in terms of m, g and h, Amanda's share of the sweets.
    b) hence, find Amanda's share of the sweets if m=20, g=2 and h=6

    Thank you in advance.
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  2. #2
    MHF Contributor

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    Re: Need Help

    The only "challenging part" is deciding if you want to try to write it as a single equation. It is simpler to write each statement as an equation.
    Let A, B, and C represent the number of sweets Amanda, Beatrice, and Christina had, respectively.
    "m sweets were shared among Amanda, Beatrice, and Chrisina." A+ B+ C= m
    "Beatrice has h/2 times as many sweets as Christina." B= (h/2)C
    "Amanda's share is g times Beatrice's share." A= gB

    Since B= (h/1)C, A= g(h/2)C= (gh/2)C. So we can write B= A/g and C= 2A/gh.

    Putting those into the first equation A+ A/g+ 2A/gh= (1+ g+ 2/gh)A= m.

    Can you solve that for A?
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  3. #3
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    Re: Need Help

    Thank you HallsofIvy for your swift reply and for taking the time to help in such a detailed way. Continuing from where you stopped....

    A = m / (1 + g + 2/gh)

    But when I substituted m=20. g=2 and h=6 into the equation, I get a fraction of 120/19. Shouldn't the answer be an integer instead of a fraction?

    Please continue to help... TIA
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