Question

In a certain class there are a total of 43 majors in mathematics, 24 majors in philosophy, and 3 students who are double-majoring in both mathematics and philosophy. Suppose that there are 531 students in the entire class. How many are majoring in neither of these subjects?

Answer 1

After accounting for double majors by subtracting them from the sum of mathematics and philosophy majors, 467 students out of 531 are found to be majoring in neither mathematics nor philosophy.

Step-by-step explanation:

To calculate how many students are majoring in neither mathematics nor philosophy, we need to account for students who are double-majoring since they are counted in both of the groups. First, we will add the total number of mathematics majors to the number of philosophy majors, then subtract the number of double majors to avoid double-counting them:

43 mathematics majors + 24 philosophy majors - 3 double majors = 64 students.

Now subtract the 64 students who are majoring in at least one of these subjects from the total number of students to find out how many are majoring in neither:

531 total students - 64 students majoring in math or philosophy = 467 students majoring in neither subject.