Difference between revisions of "2006 AMC 8 Problems/Problem 12"

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Adding them up gets <math> 7+16+27=50 </math>. The overall percentage correct would be <math> \frac{50}{60}=\frac{5}{6}=5 \cdot 16.\overline{6}=83.\overline{3} \approx \boxed{\textbf{(D)}\ 83} </math>.
 
Adding them up gets <math> 7+16+27=50 </math>. The overall percentage correct would be <math> \frac{50}{60}=\frac{5}{6}=5 \cdot 16.\overline{6}=83.\overline{3} \approx \boxed{\textbf{(D)}\ 83} </math>.
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{{AMC8 box|year=2006|num-b=11|num-a=13}}

Revision as of 14:56, 21 November 2011

Problem

Antonette gets $70 \%$ on a 10-problem test, $80 \%$ on a 20-problem test and $90 \%$ on a 30-problem test. If the three tests are combined into one 60-problem test, which percent is closest to her overall score?

$\textbf{(A)}\ 40\qquad\textbf{(B)}\ 77\qquad\textbf{(C)}\ 80\qquad\textbf{(D)}\ 83\qquad\textbf{(E)}\ 87$

Solution

$70 \% \cdot 10=7$

$80 \% \cdot 20=16$

$90 \% \cdot 30=27$

Adding them up gets $7+16+27=50$. The overall percentage correct would be $\frac{50}{60}=\frac{5}{6}=5 \cdot 16.\overline{6}=83.\overline{3} \approx \boxed{\textbf{(D)}\ 83}$.

2006 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 11
Followed by
Problem 13
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All AJHSME/AMC 8 Problems and Solutions