Difference between revisions of "2021 AMC 10A Problems/Problem 5"
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| + | ==Problem 5== | ||
| + | The quiz scores of a class with <math>k > 12</math> students have a mean of <math>8</math>. The mean of a collection of <math>12</math> of these quiz scores is <math>14</math>. What is the mean of the remaining quiz scores of terms of <math>k</math>? | ||
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| + | <math>\textbf{(A)} ~\frac{14-8}{k-12} \qquad\textbf{(B)} ~\frac{8k-168}{k-12} \qquad\textbf{(C)} ~\frac{14}{12} - \frac{8}{k} \qquad\textbf{(D)} ~\frac{14(k-12)}{k^2} \qquad\textbf{(E)} ~\frac{14(k-12)}{8k}</math> | ||
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| + | ==Solution== | ||
| + | The total score in the class is <math>8k.</math> | ||
| + | The total score on the <math>12</math> quizzes is <math>12\cdot14=168.</math> | ||
| + | Therefore, for the remaining quizzes (<math>k-12</math> of them), the total score is <math>8k-168.</math> Their mean score is <math>\boxed{\textbf{(B)} ~\frac{8k-168}{k-12}}.</math> | ||
| + | |||
== Video Solution (Using average formula) == | == Video Solution (Using average formula) == | ||
https://youtu.be/jocfZVNGU3o | https://youtu.be/jocfZVNGU3o | ||
~ pi_is_3.14 | ~ pi_is_3.14 | ||
Revision as of 21:40, 11 February 2021
Problem 5
The quiz scores of a class with 
students have a mean of 
. The mean of a collection of 
of these quiz scores is 
. What is the mean of the remaining quiz scores of terms of 
?
Solution
The total score in the class is 
The total score on the quizzes is 
Therefore, for the remaining quizzes (
of them), the total score is 
Their mean score is 
Video Solution (Using average formula)
~ pi_is_3.14
