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Difference between revisions of "2001 AMC 10 Problems/Problem 3"

(Created page with '== Problem == The sum of two numbers is <math> S </math>. Suppose <math> 3 </math> is added to each number and then each of the resulting numbers is doubled. What is the sum of …')
 
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== Solution ==
 
== Solution ==
  
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The sum of the two numbers is <math> S </math>. If <math> 3 </math> is added to each number, then you basically added <math> 6 </math> to <math> S </math>. When you double the resulting expression,  
+
The sum of the two numbers is <math> S </math>. If <math> 3 </math> is added to each number, then you basically added <math> 6 </math> to <math> S </math>.  
 +
 
 +
When you double the resulting expression,  
  
 
<math> 2(S+6) = \textbf{(E) }2S+12 </math>
 
<math> 2(S+6) = \textbf{(E) }2S+12 </math>

Revision as of 11:57, 16 March 2011

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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