2021 AMC 10A Problems/Problem 5

Problem 5

The quiz scores of a class with $k > 12$ students have a mean of $8$ . The mean of a collection of $12$ of these quiz scores is $14$ . What is the mean of the remaining quiz scores of terms of $k$ ?

$\textbf{(A)} ~\frac{14-8}{k-12} \qquad\textbf{(B)} ~\frac{8k-168}{k-12} \qquad\textbf{(C)} ~\frac{14}{12} - \frac{8}{k} \qquad\textbf{(D)} ~\frac{14(k-12)}{k^2} \qquad\textbf{(E)} ~\frac{14(k-12)}{8k}$

Solution

The total score in the class is $8k.$ The total score on the $12$ quizzes is $12\cdot14=168.$ Therefore, for the remaining quizzes ( $k-12$ of them), the total score is $8k-168.$ Their mean score is $\boxed{\textbf{(B)} ~\frac{8k-168}{k-12}}.$

Video Solution (Using average formula)

https://youtu.be/jocfZVNGU3o

~ pi_is_3.14

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2021 AMC 10A Problems/Problem 5

Problem 5

Solution

Video Solution (Using average formula)