2014 AMC 12A Problem 2

At the theater children get in for half price. The price for 5 adult tickets and 4 child tickets is \$24.50. How much would 8 adult tickets and 6 child tickets cost?

\textbf{(A) }35\qquad \textbf{(B) }38.50\qquad \textbf{(C) }40\qquad \textbf{(D) }42\qquad \textbf{(E) }42.50$

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