Question

Two hundred college students were asked where they buy their lunches. The results showed that 84 students buy their lunches in the food court in the university center, 101 students buy their lunches from a food truck and 28 students buy their lunches from both. Based on the survey, how many students buy lunch:

Answer 1

By applying the principle of inclusion-exclusion, we find that 157 of the surveyed 200 college students buy their lunches from either the food court in the university center or from a food truck.

Step-by-step explanation:

To determine how many students buy lunch either at the food court in the university center or from a food truck, we can use the principle of inclusion-exclusion. The total number of students buying lunch is the sum of those buying at the food court and those buying from the food truck minus those who buy their lunches at both places to avoid double-counting.

We have 84 students who buy their lunches in the food court, 101 students who buy them from a food truck, and 28 students who buy their lunches from both. So using the formula:

Total number of students buying lunch = (Students at food court) + (Students at food truck) - (Students at both)

Substituting the numbers we have:

Total number of students buying lunch = 84 + 101 - 28 = 157 students.

This means out of the 200 surveyed, 157 students buy their lunches from either the food court or the food truck.

Answer 2

The students buys the lunch = 157

Step-by-step explanation:

Students buy their lunches in the food court in the university center = 84

Students buy their lunches from a food truck = 101

Students buy their lunches from both = 28

Students buy their lunches either from the food court in the university center or from a food truck = (Students buy their lunches in the food court in the university center) + (Students buy their lunches from a food truck) - (Students buy their lunches from both)

⇒ 84 + 101- 28 = 157

Thus the students buys the lunch = 157