There are 16 red, 16 blue and 16 yellow marbles in a jar. What is the fewest marbles you can remove from the jar so that the ratio of red to non-red marbles is 13 to 29 and the ratio of yellow to non-yellow marbles is 13 to 29?
We must end up with a multiple of 13 reds and a multiple of 13 yellows.
Since we only have 16 of each, the only possible multiple of 13 we
could have of each is 13 itself. So it is only possible that we remove
3 reds and 3 yellows.
To have the desired ratio, we must end up with 29 non-reds and 29
non-yellows. So let's see how many, if any blue marbles we need to
remove to have 29 non-reds and 29 non-yellows. It turns out that we
already have 29 of each of these since 13+16=29. So we don't need to
remove any blue marbles.
Answer: Remove 3 reds and 3 yellows only. Then we have 13 reds, 13 yellows,
13+16 or 29 non-reds and 13+15=29 non-yellows.
Edwin