2006 Cayley Problem 20

The line y = -\frac{3}{4}x + 9 crosses the x-axis at P and the y-axis at Q. Point T(r,\ \text{s}) is on line segment PQ. If the area of \triangle POQ is three times the area of \triangle TOP, then the value of r + s is

\textbf{(A)}\ 7\quad \textbf{(B)}\ 10\quad \textbf{(C)}\ 11\quad \textbf{(D)}\ 14\quad \textbf{(E)}\ 18

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.