AMC 8 1987 Problem 16

Joyce made $12$ of her first $30$ shots in the first three games of this basketball game, so her seasonal shooting average was $40\%$. In her next game, she took $10$ shots and raised her seasonal shooting average to $50\%$. How many of these $10$ shots did she make? $\text{(A)}\ 2 \text{(B)}\ 3 \text{(C)}\ 5 \text{(D)}\ 6 \text{(E)}\ 8$