The students in Mr. Neatkin's class took a penmanship test. Two-thirds of the boys and $\frac{3}{4}$ of the girls passed the test, and an equal number of boys and girls passed the test. What is the minimum possible number of students in the class?
$\textbf{(A)}\ 12\qquad \textbf{(B)}\ 17\qquad \textbf{(C)}\ 24\qquad \textbf{(D)}\ 27\qquad \textbf{(E)}\ 36$
Let $b$ be the number of boys and $g$ be the number of girls.
\[\frac23 b = \frac34 g \Rightarrow b = \frac98 g\]
For $g$ and $b$ to be integers, $g$ must cancel out with the denominator, and the smallest possible value is $8$. This yields $9$ boys. The minimum number of students is $8+9=\boxed{\textbf{(B)}\ 17}$.