Problem:
After Euclid High School's last basketball game, it was determined that of the team's points were scored by Alexa and were scored by Brittany. Chelsea scored points. None of the other team members scored more than points. What was the total number of points scored by the other team members?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the total number of points and be the desired answer. Then, from the problem statement, we get the equation:
Simplifying this, we get:
We know that since none of the team members scored more than points. We also know that must be a multiple of . If , then we get:
which is not allowed. If , then we have:
which works.
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions