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Math Help - Ratio help

  1. #1
    pri
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    Angry Ratio help

    1/5 of chicken John had is equal to 3/4 of Mark.
    John sold 150 chickens while Mark bought 160.
    The remider is in a ratio of 5:3, for John & Mark respectively.
    What was the total number of chickens both had at first.
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  2. #2
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    Quote Originally Posted by pri View Post
    1/5 of chicken John had is equal to 3/4 of Mark.
    John sold 150 chickens while Mark bought 160.
    The remider is in a ratio of 5:3, for John & Mark respectively.
    What was the total number of chickens both had at first.
    Let J be the amount John had at the start, and let M be the amount Mark had at the start.
    So J/5 = 3M/4

    Then if J' is the amount that John had after the buying and selling, and M' is the amount Mark had after buying and selling, then the 5:3 ratio tells us that
    3J'/8 = 5M'/8

    We also know that J' = J - 150
    and M' = M + 160.

    So if we replace J' and M' with those
    we get:
    \frac{3(J - 150)}{8} = \frac{5(M + 160)}{8}

    So we have two simultaneous equations with two unknowns:
    \frac{3(J - 150)}{8} = \frac{5(M + 160)}{8}
    \frac{J}{5} = \frac{3M}{4}

    And solve...
    Last edited by Unenlightened; April 29th 2009 at 09:04 AM. Reason: tags tags tags...
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  3. #3
    Senior Member Twig's Avatar
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    hi

    hi!

    Let  C_{j} \mbox{ and } C_{m} be notations for chickens for John and for Mark.

    We have that:

     \frac{1}{5}C_{j}=\frac{3}{4}C_{m} \Rightarrow 4C_{j}-15C_{m}=0

    We have also:

     \frac{C_{j}-150}{C_{m}+160}=\frac{5}{3} \Rightarrow 3C_{j}-5C_{m}=1250

    So, you have two equations and two unknowns. Can you proceed from here?
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