2001 AMC 10 Problems/Problem 3

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?

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

Solution

The sum of the two numbers is $S$ . If $3$ is added to each number, then you basically added $6$ to $S$ .

When you double the resulting expression,

$2(S+6) = \textbf{(E) }2S+12$

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2001 AMC 10 Problems/Problem 3

Problem

Solution