AMC 8 1987 Problem 18

Half the people in a room left. One third of those remaining started to dance. There were then $12$ people who were not dancing. The original number of people in the room was $\text{(A)}\ 24 \text{(B)}\ 30 \text{(C)}\ 36 \text{(D)}\ 42 \text{(E)}\ 72$