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?
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.
