Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 1"
I_like_pie (talk | contribs) m |
|||
(4 intermediate revisions by 2 users not shown) | |||
Line 1: | Line 1: | ||
== 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. |
− | + | ---- | |
− | * [[University of South Carolina High School Math Contest/1993 Exam]] | + | |
+ | * [[University of South Carolina High School Math Contest/1993 Exam/Problem 2|Next Problem]] | ||
+ | * [[University of South Carolina High School Math Contest/1993 Exam|Back to Exam]] | ||
+ | |||
+ | [[Category:Introductory Geometry Problems]] | ||
+ | [[Category:Introductory Algebra Problems]] |