Two high school classes took the same test. One class of $20$ students made an average grade of $80\%$; the other class of $30$ students made an average grade of $70\%$. The average grade for all students in both classes is:
$\textbf{(A)}\ 75\%\qquad \textbf{(B)}\ 74\%\qquad \textbf{(C)}\ 72\%\qquad \textbf{(D)}\ 77\%\qquad \textbf{(E)\ }\text{none of these}$
The desired average can be found by dividing the total number of points earned by the total number of students. There are $20\cdot 80+30\cdot 70=3700$ points earned and $20+30=50$ students. Thus, our answer is $\frac{3700}{50}$, or $\boxed{\textbf{(B)}\ 74\%}$.