Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 1"
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== Problem == | == 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? | + | 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? |
<center><math> \mathrm{(A) \ } 1 \qquad \mathrm{(B) \ } 2 \qquad \mathrm{(C) \ } 3 \qquad \mathrm{(D) \ } 6 \qquad \mathrm{(E) \ } 9 </math></center> | <center><math> \mathrm{(A) \ } 1 \qquad \mathrm{(B) \ } 2 \qquad \mathrm{(C) \ } 3 \qquad \mathrm{(D) \ } 6 \qquad \mathrm{(E) \ } 9 </math></center> | ||
== Solution == | == Solution == | ||
− | Let <math>a</math> be the length and <math>b</math> be the width. We have that <math>3ab=2b(a+3) \Longrightarrow ab= | + | Let <math>a</math> be the length and <math>b</math> be the width. We have that <math>3ab=2b(a+3) \Longrightarrow ab=6b</math>. Dividing by <math>b</math> give <math>a=6</math> so <math>\mathrm{(D)</math> is our answer. |
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Revision as of 17:17, 17 August 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?
![$\mathrm{(A) \ } 1 \qquad \mathrm{(B) \ } 2 \qquad \mathrm{(C) \ } 3 \qquad \mathrm{(D) \ } 6 \qquad \mathrm{(E) \ } 9$](http://latex.artofproblemsolving.com/b/f/3/bf3cf45fe611d0698538a185c14d41a0d91220e5.png)
Solution
Let be the length and
be the width. We have that
. Dividing by
give
so $\mathrm{(D)$ (Error compiling LaTeX. Unknown error_msg) is our answer.