2023 AMC 12A Problem 8

Problem 8 of 25EasierAlgebra

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?

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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.