Problem:
In a high school with students, of the seniors play a musical instrument, while of the non-seniors do not play a musical instrument. In all, of the students do not play a musical instrument. How many non-seniors play a musical instrument?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the number of non-seniors. Because there are students in all, there are seniors. Because of the seniors play a musical instrument, of the seniors do not play a musical instrument. This leads to the equation
The equation simplifies to . Solving this equation for gives . Because of the non-seniors play a musical instrument, there are non-seniors who play a musical instrument.
The problems on this page are the property of the MAA's American Mathematics Competitions