2013 Fermat Problem 24

In the diagram, \triangle PQR has S on PR and V on RQ. Segments QS and PV intersect at T. Segments RT and SV intersect at U. If the area of \triangle RST is 55, the area of \triangle RTV is 66, and the area of \triangle RSV is 77, then the area of \triangle PQU is

\textbf{(A)}\ 869\quad \textbf{(B)}\ 836\quad \textbf{(C)}\ 840\quad \textbf{(D)}\ 864\quad \textbf{(E)}\ 847

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

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