Question

150 college freshmen were interviewed. 85 were registered for a math class, 70 were registered for an English class, 50 were registered for both math and English. Answer the following:

1. How many signed up only for a math class?
2. How many signed up only for an English class?
3. How many signed up for math or English?
4. How many signed up for neither math nor English?

Answer 1

To find the number of students signed up only for a math class, subtract the number of students signed up for both math and English from the total number of students signed up for a math class.

Step-by-step explanation:

To solve this problem, we can use the principle of inclusion-exclusion. Let's represent the number of students signed up for a math class as A, the number of students signed up for an English class as B, and the number of students signed up for both math and English as C.

1. To find the number of students signed up only for a math class, we can subtract the number of students signed up for both math and English (C) from the total number of students signed up for a math class (A). So, the number of students signed up only for a math class is A - C = 85 - 50 = 35.
2. To find the number of students signed up only for an English class, we can subtract the number of students signed up for both math and English (C) from the total number of students signed up for an English class (B). So, the number of students signed up only for an English class is B - C = 70 - 50 = 20.
3. To find the number of students signed up for math or English, we can add the number of students signed up only for a math class (35), the number of students signed up only for an English class (20), and the number of students signed up for both math and English (50). So, the number of students signed up for math or English is 35 + 20 + 50 = 105.
4. To find the number of students signed up for neither math nor English, we can subtract the number of students signed up for math or English (105) from the total number of students (150). So, the number of students signed up for neither math nor English is 150 - 105 = 45.