Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 2"

Revision as of 15:13, 29 July 2006

Suppose the operation $\star$ is defined by $a \star b = a+b+ab.$ If $3\star x = 23,$ then $x =$

$\mathrm{(A) \ } 2 \qquad \mathrm{(B) \ }3\qquad \mathrm{(C) \ }4 \qquad \mathrm{(D) \ }5 \qquad \mathrm{(E) \ }6$

$3 \star x = 23 \Longrightarrow 3+x+3x=23 \Longrightarrow 4x = 20 \Longrightarrow x=5$ , so the answer is $\mathrm{(D) \ }$ .

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 == Problem ==
-Suppose the operation <math>\star</math> is defined by <math>a \star b = a+b+ab.</math> If <math>3\star x = 23,</math> then <math>x =</math>
+Suppose the [[operation]] <math>\star</math> is defined by <math>a \star b = a+b+ab.</math> If <math>3\star x = 23,</math> then <math>x =</math>
 <center><math> \mathrm{(A) \ } 2 \qquad \mathrm{(B) \ }3\qquad \mathrm{(C) \ }4 \qquad \mathrm{(D) \ }5 \qquad \mathrm{(E) \ }6  </math></center>
 == Solution ==
-<math>3+x+3x=23 \Longrightarrow x=5</math>.
+<math>3 \star x = 23 \Longrightarrow 3+x+3x=23 \Longrightarrow 4x = 20 \Longrightarrow x=5</math>, so the answer is <math>\mathrm{(D) \ }</math>.
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