1964 AHSME Problem 23

Two numbers are such that their difference, their sum, and their product are to one another as 1:7:24. The product of the two numbers is:

\textbf{(A)}\ 6\qquad \textbf{(B)}\ 12\qquad \textbf{(C)}\ 24\qquad \textbf{(D)}\ 48\qquad \textbf{(E)}\ 96

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