Problem:
Maureen is keeping track of the mean of her quiz scores this semester. If Maureen scores an on the next quiz, her mean will increase by . If she scores an on each of the next three quizzes, her mean will increase by . What is the mean of her quiz scores currently?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Suppose Maureen has taken quizzes so far, with mean . Then
These two equations simplify to and , respectively. Subtracting twice the first equation from the second equation yields , so . Then , so Maureen has taken 3 quizzes so far, and their scores could, for example, be 6,7 , and 8 . Then one score of 11 increases the mean to
and three scores of 11 increase the mean to
The problems on this page are the property of the MAA's American Mathematics Competitions