2025 Cayley Problem 3

In the diagram, the large rectangle is divided into 9 smaller rectangles. Each of the 5 smaller shaded rectangles has a width of 4 and each of the 4 smaller unshaded rectangles has a width of 8. The width, w, of the large rectangle is

\textbf{(A)}\ 20\quad \textbf{(B)}\ 32\quad \textbf{(C)}\ 52\quad \textbf{(D)}\ 56\quad \textbf{(E)}\ 68

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.