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University of South Carolina High School Math Contest/1993 Exam/Problem 1

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 $3ab=2b(a+3) \Longrightarrow ab=6b$. Dividing by $b$ yields $a=6$ so $\mathrm{(D)}$ is our answer.


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