2023 AMC 12A Problem 8

Attempt Problem 8 of the 2023 AMC 12A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2023 AMC 12A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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

Let her current mean be

m

over

n

quizzes, with total

S=mn

One extra

11

gives

\dfrac{S+11}{n+1}=m+1;

simplify to

m+n=10

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.

Problem 8 in other years