Joyce made $12$ of her first $30$ shots in the first three games of this basketball game, so her seasonal shooting [average](https://artofproblemsolving.com/wiki/index.php/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?
$\text{(A)}\ 2 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 6 \qquad \text{(E)}\ 8$
After the fourth game, she took $40$ shots, $50\%$ of which she made, so she made $40\times .5=20$ shots.  Twelve of them were made in the first three games, so in the last game she made $20-12=8$ shots.
$\boxed{\text{E}}$