Problem:
At a math contest, 57 students are wearing blue shirts, and another 75 students are wearing yellow shirts. The 132 students are assigned into 66 points. In exactly 23 of these pairs, both students are wearing blue shirts. In how many pairs are both students wearing yellow shirts?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are students paired with a blue partner. The other students wearing blue shirts must each be paired with a partner wearing a shirt of the opposite color. There are students remaining. Therefore the requested number of pairs is .
The problems on this page are the property of the MAA's American Mathematics Competitions