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Thread: multiplying ratios without knowing the ratios?

  1. #1
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    multiplying ratios without knowing the ratios?

    This problem is verbatim out of the text book.

    There is a number of balls in a jar. EAch ball is painted with at least one of twocolors, red or green. It is observed that 2/7 of the balls that have red color also have green color, while 3/7 of the balls that have green color also have red color. What fraction of the balls in the jar have both red and green colors?

    I understand that the numerator is some factor of seven, but the answer they give in the book makes no sense to me at all.

    I dont see how this can be solved without knowing the ratio of green to red, and I see the math in the book but it simply makes no sense to me.

    thanks in advance to anyone who can help
    Last edited by NotTooKeen; Sep 28th 2009 at 01:15 AM.
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    Quote Originally Posted by NotTooKeen View Post
    There is a number of balls in a jar. EAch ball is painted with at least one of twocolors, red or green. It is observed that 2/7 of the balls that have red color also have green color, while 3/7 of the balls that have green color also have red color. What fraction of the balls in the jar have both red and green colors?
    Suppose that $\displaystyle G$ is the number of balls having green on them.
    Suppose that $\displaystyle R$ is the number of balls having red on them.
    Suppose that $\displaystyle B$ is the number of balls having both colors on them.

    Now we are given that $\displaystyle R = \frac{{7B}}{2}\;\& \,G = \frac{{7B}}{3}$.
    The total number of balls is $\displaystyle R+G-B$.
    Using that we can get that the fraction of the balls in the jar have both red and green colors is $\displaystyle \frac{6}{29}$.
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