2011 AMC 12B Problems/Problem 2

Problem

Josanna's test scores to date are $90, 80, 70, 60,$ and $85.$ Her goal is to raise her test average at least $3$ points with her next test. What is the minimum test score she would need to accomplish this goal?

$\textbf{(A)}\ 80 \qquad \textbf{(B)}\ 82 \qquad \textbf{(C)}\ 85 \qquad \textbf{(D)}\ 90 \qquad \textbf{(E)}\ 95$

Solution

Take the average of her current test scores, which is $\frac{90+80+70+60+85}{5} = \frac{385}{5} = 77$

This means that she wants her test average after the sixth test to be $80.$ Let $x$ be the score that Josanna receives on her sixth test. Thus, our equation is

$\frac{90+80+70+60+85+x}{6} = 80$

$385+x = 480$

\[x = \boxed{95\  \(\textbf{(E)}}\] (Error compiling LaTeX. Unknown error_msg)

2011 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 1	Followed by Problem 3
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All AMC 12 Problems and Solutions

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2011 AMC 12B Problems/Problem 2

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