2001 AMC 12 Problems/Problem 1

Problem

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?

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

Solution

Suppose the two numbers are $a$ and $b$ , with $a+b=S$ . Then the desired sum is $2(a+3)+2(b+3)=2(a+b)+12=2S +12$ , which is answer $\text{(E)}$ .

2001 AMC 12 (Problems • Answer Key • Resources)
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2001 AMC 12 Problems/Problem 1

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