If $\frac{3}{5}=\frac{M}{45}=\frac{60}{N}$, what is $M+N$?
$\textbf{(A)}\ 27\qquad \textbf{(B)}\ 29 \qquad \textbf{(C)}\ 45 \qquad \textbf{(D)}\ 105\qquad \textbf{(E)}\ 127$
Separate into two equations $\frac35 = \frac{M}{45}$ and $\frac35 = \frac{60}{N}$ and solve for the unknowns. $M=27$ and $N=100$, therefore $M+N=\boxed{\textbf{(E)}\ 127}$.