The entire contents of a jug can exactly fill 9 small glasses and 4 large glasses of juice. The entire contents of the jug could instead fill 6 small glasses and 6 large glasses. If the entire contents of the jug is used to fill only large glasses, the maximum number of large glasses that can be filled is
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Let the volume of a large glass be $L$ and of a small glass be $S$. Since the jug can exactly fill either 9 small glasses and 4 large glasses, or 6 small glasses and 6 large glasses, then $9 S+4 L=6 S+6 L$ or $3 S=2 L$. In other words, the volume of 3 small glasses equals the volume of 2 large glasses. (We can also see this without using algebra - if we compare the two cases, we can see that if we remove 3 small glasses then we increase the volume by 2 large glasses.) Therefore, the volume of 9 small glasses equals the volume of 6 large glasses. Thus, the volume of 9 small glasses and 4 large glasses equals the volume of 6 large glasses and 4 large glasses, or 10 large glasses in total, and so the jug can fill 10 large glasses in total.

Answer: (C)