How many students ar e taking neither of these two courses, i.e. neither statistics nor economics?

Question

A small college has 987 students. 54 are enrolled in statistics, 45 are enrolled in economics, and 15 are enrolled in both statistics and economics. How many students are taking neither of these two courses, i.e. neither statistics nor economics?

Answer 1

Use a Venn diagram to make it clear! There are 987 students, 45 are taking economics, and 54 are taking statistics. 

The circle labeled statistics has has 54 students, the circle labeled economics has  has 45 students. The intersection has 15 which represents students taking BOTH.

We don't want to count them twice!

Let x be the number of students taking neither:

39 +15 +30 +x =987

x=903

There are 903 students who take neither.