Problem:
Ms. Blackwell gives an exam to two classes. The mean of the scores of the students in the morning class is , and the afternoon class mean score is . The ratio of the number of students in the morning class to the number of students in the afternoon class is . What is the mean of the scores of all the students?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Answer (C): Let be the number of students in the morning class and the number of students in the afternoon class. It is given that , so . The total number of points scored by all students is , so the requested mean is
OR
The requested value is just the weighted average of 84 and 70 , with weights 3 and 4 :
The problems on this page are the property of the MAA's American Mathematics Competitions