1999 Gauss 8 Problem 16

In a set of five numbers, the average of two of the numbers is 12 and the average of the other three numbers is 7. The average of all five numbers is

\textbf{(A)}\ 8\frac{1}{3}\quad \textbf{(B)}\ 8\frac{1}{2}\quad \textbf{(C)}\ 9\quad \textbf{(D)}\ 8\frac{3}{4}\quad \textbf{(E)}\ 9\frac{1}{2}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.