AMC 12 2001 Problem 1

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?

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