2001 AMC 10 Problem 3

The sum of two numbers is S. Suppose 3 is added to each number and then each of the resulting numbers is doubled. What is the sum of the final two numbers?

\textbf{(A) } 2S+3 \qquad\textbf{(B) } 3S+2 \qquad\textbf{(C) } 3S+6 \qquad\textbf{(D) } 2S+6 \qquad\textbf{(E) } 2S+12

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