An Annville Junior High School, $30\%$ of the students in the Math Club are in the Science Club, and $80\%$ of the students in the Science Club are in the Math Club.  There are 15 students in the Science Club.  How many students are in the Math Club?
$\text{(A)}\ 12 \qquad \text{(B)}\ 15 \qquad \text{(C)}\ 30 \qquad \text{(D)}\ 36 \qquad \text{(E)}\ 40$
If $80\%$ of the people in the science club of $15$ people are in the Math Club, $\frac{4}{5}\times15=12$ people are in the both the Math Club and the Science Club.
These $12$ people make up $30\%$ of the Math Club.
Setting up a proportion:
$12\cdot 1.00 =0.30\cdot x$
$\frac{12}{0.3} = 40=x$
There are $40=\boxed{E}$ people in the Math Club.