1967 AHSME Problem 19

The area of a rectangle remains unchanged when it is made 2 \frac{1}{2} inches longer and \frac{2}{3} inch narrower, or when it is made 2 \frac{1}{2} inches shorter and \frac{4}{3} inch wider. Its area, in square inches, is:

\textbf{(A)}\ 30\qquad \textbf{(B)}\ \frac{80}{3}\qquad \textbf{(C)}\ 24\qquad \textbf{(D)}\ \frac{45}{2}\qquad \textbf{(E)}\ 20

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.