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Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 1"

 
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== See also ==
 
== See also ==
 
* [[University of South Carolina High School Math Contest/1993 Exam]]
 
* [[University of South Carolina High School Math Contest/1993 Exam]]
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[[Category:Introductory Geometry Problems]]
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[[Category:Introductory Algebra Problems]]

Revision as of 20:42, 22 July 2006

Problem

If the width of a particular rectangle is doubled and the length is increased by 3, then the area is tripled. What is the length of the rectangle?

$\mathrm{(A) \ } 1 \qquad \mathrm{(B) \ } 2 \qquad \mathrm{(C) \ } 3 \qquad \mathrm{(D) \ } 6 \qquad \mathrm{(E) \ } 9$

Solution

Let $a$ be the length and $b$ be the width. We have that $3ab=2b(a+3) \Longrightarrow ab=6$. $a=6, b=1$ works, so $6$ is our answer.

See also

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