2023 AMC 10A Problem 10

Problem 10 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?

Show solution

Solution

Let

m

be the current mean over

n

quizzes. One more

11

makes the mean

m + 1:

\frac{mn + 11}{n + 1} = m + 1,

which tidies up to

m + n = 10.

Three more

11

s make it

m + 2:

\frac{mn + 33}{n + 3} = m + 2,

i.e.

3m + 2n = 27.

Solve the pair and

m = 7.

Therefore, the answer is D.