AMC 12 2012b Problem 17

Square $PQRS$ lies in the first quadrant. Points $(3,0), (5,0), (7,0),$ and $(13,0)$ lie on lines $SP, RQ, PQ,$ and $SR$, respectively. What is the sum of the coordinates of the center of the square $PQRS$?

\textbf{(A)}\ 6 \textbf{(B)}\ \frac{31}{5} \textbf{(C)}\ \frac{32}{5} \textbf{(D)}\ \frac{33}{5} \textbf{(E)}\ \frac{34}{5}