# Math Help - multiplying ratios without knowing the ratios?

1. ## 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

2. Originally Posted by NotTooKeen
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 $G$ is the number of balls having green on them.
Suppose that $R$ is the number of balls having red on them.
Suppose that $B$ is the number of balls having both colors on them.

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