Question

Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an $11$ on the next quiz, her mean will increase by $1.$ If she scores an $11$ on each of the next three quizzes, her mean will increase by $2.$ What is the mean of her quiz scores currently?

$4$

$5$

$6$

$7$

$8$

Answer: D

Concepts:mean system of equations

Difficulty rating: 1440

Solution:

Let the current mean be $m$ over $n$ quizzes, so the total is $S=mn.$ Adding one $11$ gives $\dfrac{mn+11}{n+1}=m+1,$ which simplifies to $m+n=10.$

Adding three $11$ 's gives $\dfrac{mn+33}{n+3}=m+2,$ which simplifies to $3m+2n=27.$

Solving $m+n=10$ and $3m+2n=27$ gives $m=7.$

Thus, the correct answer is D.

2023 AMC 12A Problem 8

Answer: D

Difficulty rating: 1440

Solution:

Problem 8 in Other Years