6. At a party, every boy danced with 4 different girls and every girl danced with 3 different boys. Knowing that there were 9 boys at the party, how many girls were there?
(A) 6
(B) 10
(C) 12
(D) 8
(E) 16
Problem 6. The answer is (C).

Let $m$ and $f$ be the number of boys and the number of girls present at the party, respectively. The number of pairs (boy, girl) who were seen dancing is, by hypothesis, equal to $4m = 3f$; since $m = 9$, it follows that $f = \frac{4}{3} m = 12$.

(Problem proposed by F. Getman)