AHSME 1967 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: $\textbf{(A)}\ 30 \textbf{(B)}\ \frac{80}{3} \textbf{(C)}\ 24 \textbf{(D)}\ \frac{45}{2} \textbf{(E)}\ 20$