Susie pays for $4$ muffins and $3$ bananas. Calvin spends twice as much paying for $2$ muffins and $16$ bananas. A muffin is how many times as expensive as a banana?
$\textbf{(A)}\ \frac{3}{2}\qquad\textbf{(B)}\ \frac{5}{3}\qquad\textbf{(C)}\ \frac{7}{4}\qquad\textbf{(D)}\ 2\qquad\textbf{(E)}\ \frac{13}{4}$
Let $m$ stand for the cost of a muffin, and let $b$ stand for the value of a banana.  We we need to find $\frac{m}{b}$, the ratio of the price of the muffins to that of the bananas. We have
\[2(4m + 3b) = 2m + 16b\]
\[6m = 10b\]
\[\frac{m}{b} = \boxed{\textbf{(B)}\ \frac{5}{3}}\]