1978 AHSME Problem 5

Four boys bought a boat for \$60. The first boy paid one half of the sum of the amounts paid by the other boys; the second boy paid one third of the sum of the amounts paid by the other boys; and the third boy paid one fourth of the sum of the amounts paid by the other boys. How much did the fourth boy pay?

\textbf{(A) }\$10\qquad \textbf{(B) }\$12\qquad \textbf{(C) }\$13\qquad \textbf{(D) }\$14\qquad \textbf{(E) }\$15

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