math

An amount of $9000 is divided among four persons A,B,C and D. The sum of shares of A,C and D is four times the share of B. The sum of shares of B and D is equal to four-fifths the sum of shares of A and C. Find the share of D.

Please help!! How to frame equation for share of each person?

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  1. just write the data as given:

    a+b+c+d = 9000
    a+c+d = 4b
    b+d = 4/5 (a+c)

    The first says that
    a+c+d = 9000-b
    using the second, that means that
    9000-b = 4b
    b = 1800

    So, now we have
    a+c+d = 7200
    1800+d = 4/5 (a+c)

    Now we know that
    a+d = 7200-d, so
    1800+d = 4/5 (7200-d)
    1800+d = 5760 - 4/5 d
    9/5 d = 3960
    d = 2200

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  2. Thank you very much. Explained neat and wast. I was breaking my head for this.

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  3. *neat and good

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  4. typing error
    this line a+d = 7200-d, so should be,

    a+c=7200-d

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