Difference between revisions of "2011 AMC 12B Problems/Problem 2"

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Josanna's test scores to date are <math>90, 80, 70, 60,</math> and <math>85.</math> Her goal is to raise her test average at least <math>3</math> points with her next test. What is the minimum test score she would need to accomplish this goal?
 
Josanna's test scores to date are <math>90, 80, 70, 60,</math> and <math>85.</math> Her goal is to raise her test average at least <math>3</math> points with her next test. What is the minimum test score she would need to accomplish this goal?
 
   
 
   
<math>
+
<math>\textbf{(A)}\ 80 \qquad
\textbf{(A)}\ 80 \qquad
 
 
\textbf{(B)}\ 82 \qquad
 
\textbf{(B)}\ 82 \qquad
 
\textbf{(C)}\ 85 \qquad
 
\textbf{(C)}\ 85 \qquad
 
\textbf{(D)}\ 90 \qquad
 
\textbf{(D)}\ 90 \qquad
 
\textbf{(E)}\ 95 </math>
 
\textbf{(E)}\ 95 </math>
 
  
 
== Solution ==
 
== Solution ==

Latest revision as of 13:12, 19 January 2021

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

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

\[385+x = 480\]

\[x = \boxed{95 \textbf{(E)}}\]

See also

2011 AMC 12B (ProblemsAnswer KeyResources)
Preceded by
Problem 1
Followed by
Problem 3
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions

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