2001 AMC 12 Problems/Problem 1

The following problem is from both the 2001 AMC 12 #1 and 2001 AMC 10 #3, so both problems redirect to this page.

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?

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

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 $\boxed{\textbf{(E)}}$ .

Video Solution by Daily Dose of Math

https://youtu.be/FxFb_QALttI?si=qUQVUkuBeK1cRbtS

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2001 AMC 12 (Problems • Answer Key • Resources)
Preceded by First question	Followed by Problem 2
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All AMC 12 Problems and Solutions

2001 AMC 10 (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

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2001 AMC 12 Problems/Problem 1

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Problem

Solution

Video Solution by Daily Dose of Math

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