Difference between revisions of "University of South Carolina High School Math Contest/1993 Exam/Problem 2"
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== Problem == | == 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> | <center><math> \mathrm{(A) \ } 2 \qquad \mathrm{(B) \ }3\qquad \mathrm{(C) \ }4 \qquad \mathrm{(D) \ }5 \qquad \mathrm{(E) \ }6 </math></center> | ||
== Solution == | == 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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