Problem:
A teacher gave a test to a class in which of the students are juniors and are seniors. The average score on the test was . The juniors all received the same score, and the average score of the seniors was . What score did each of the juniors receive on the test?
Answer Choices:
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Solution:
Let be the number of students in the class. Then there are juniors and seniors. Let be the score of each junior. The scores totaled , so
Note: In this problem, we could assume that the class has one junior and nine seniors. Then
The problems and solutions on this page are the property of the MAA's American Mathematics Competitions