1987 AJHSME 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 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.