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> yields <math>a=6</math> so <math>\mathrm{(D)}</math> is our answer. |
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be the length and 
be the width. We have that 
. Dividing by 
so 
is our answer.
