Thread: 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

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 is the number of balls having green on them.
Suppose that is the number of balls having red on them.
Suppose that is the number of balls having both colors on them.

Now we are given that .
The total number of balls is .
Using that we can get that the fraction of the balls in the jar have both red and green colors is .