2019 AMC 8
Complete problem set with solutions and individual problem pages
The eighth grade class at Lincoln Middle School has students. Each student takes a math class or a foreign language class or both. There are eighth graders taking a math class, and there are eighth graders taking a foreign language class. How many eighth graders take only a math class and not a foreign language class?
- A.
- B.
- C.
- D.
- E.
Solution 1
Let be the number of students taking both a math and a foreign language class.
By P-I-E, we get = .
Solving gives us .
But we want the number of students taking only a math class,
which is .
Solution 2
We have people taking classes. However, we over-counted the number of people who take both classes. If we subtract the original amount of people who take classes we get that people took the two classes. To find the amount of people who took only math class, we subtract the people who didn't take only one math class, so we get .
