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Thread: A is two-third of the sum of B and C. B is three-quarter of the sum of A and C.

  1. #1
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    Exclamation A is two-third of the sum of B and C. B is three-quarter of the sum of A and C.

    A is two-third of the sum of B and C. B is three-quarter of the sum of A and C. Express A as a fraction of B.
    Last edited by mr fantastic; Jun 7th 2010 at 04:49 AM. Reason: Re-titled.
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  2. #2
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    Simultaneous equations

    Hello dtay

    Welcome to Math Help Forum!
    Quote Originally Posted by dtay View Post
    A is two-third of the sum of B and C. B is three-quarter of the sum of A and C. Express A as a fraction of B.
    You need to create two equations involving $\displaystyle A, B$ and $\displaystyle C$, and then eliminate $\displaystyle C$ to find an equation involving just $\displaystyle A$ and $\displaystyle B$.

    Here are some clues:

    The first statement can be written: $\displaystyle A = \tfrac23(B+C)$

    So if we multiply by $\displaystyle 3: 3A = 2B+2C$

    $\displaystyle \Rightarrow C = \tfrac32A - B$ (1)

    Now write down the second statement in a similar way, and use equation (1) to eliminate $\displaystyle C$.

    Then re-arrange so that you have $\displaystyle A$ on one side, and $\displaystyle B$ on the other. Finally, divide both sides by $\displaystyle B$ to find $\displaystyle \frac{A}{B}$. I get the answer:

    $\displaystyle \frac{A}{B}= \frac{14}{15}$

    Can you fill in the gaps?

    Grandad
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  3. #3
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    Smile

    Thank You very much, Grandad.
    I understand it already, and i also have found out another method, using
    common ratio.
    I'm sorry i wasn't able to thank you earlier.
    Thank you very much for helping me!
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