2015 Cayley Problem 10

In the diagram, square PQRS is 3 \times 3. Points T and U are on side QR with QT = TU = UR = 1. Points V and W are on side RS with RV = VW = WS = 1. Line segments TX and UY are perpendicular to QR and line segments VY and WX are perpendicular to RS. The ratio of the shaded area to the unshaded area is

\textbf{(A)}\ 2:1\quad \textbf{(B)}\ 7:3\quad \textbf{(C)}\ 7:4\quad \textbf{(D)}\ 5:4\quad \textbf{(E)}\ 3:1

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.