Math CentralQuandaries & Queries


Question from Md., a student:

In a group of 15, 7 have Red Balls, 8 have Blue Balls and 3 have neither.
What fraction of the group has both Red Balls and Blue Balls?

Hi there.

Start crossing off members of the group.

If 3 have neither, that means there are 15-3 = 12 members of the group left.

7 of those members have red balls. That leaves 12-7 = 5 members who have just blue balls.

But you've been told there are 8 members with blue balls, so 8-5 = 3 more members must have blue balls and the only members who could have them already have red balls.

Stephen La Rocque

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