2019 Pascal Problem 25

In the diagram, PR and QS intersect at V. Also, W is on PV, U is on PS and T is on PQ with QU and ST passing through W. For some real number x,

- the area of \triangle PUW equals 4x + 4, - the area of \triangle SUW equals 2x + 20, - the area of \triangle SVW equals 5x + 20, - the area of \triangle SVR equals 5x + 11, - the area of \triangle QVR equals 8x + 32, and - the area of \triangle QVW equals 8x + 50.

The area of \triangle PTW is closest to

\textbf{(A)}\ 35\quad \textbf{(B)}\ 34\quad \textbf{(C)}\ 33\quad \textbf{(D)}\ 32\quad \textbf{(E)}\ 31

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 Pascal contests here.