1998 Pascal Problem 24

Three rugs have a combined area of 200 \text{ m}^2. By overlapping the rugs to cover a floor area of 140 \text{ m}^2, the area which is covered by exactly two layers of rug is 24 \text{ m}^2. What area of floor is covered by three layers of rug?

\textbf{(A)}\ 12 \text{ m}^2\quad \textbf{(B)}\ 18 \text{ m}^2\quad \textbf{(C)}\ 24 \text{ m}^2\quad \textbf{(D)}\ 36 \text{ m}^2\quad \textbf{(E)}\ 42 \text{ m}^2

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.