A college survey was taken to determine where students study. Of 104 students surveyed, 60 studied in the cafeteria , 53 studied in the student lounge , 20 studied in both the cafeteria and the student lounge.
To find out how many students studied either in the cafeteria or the student lounge, we need to apply the principle of inclusion-exclusion.
Step 1: Find the total number of students who studied in either the cafeteria or the student lounge. This can be done by adding the number of students who studied in the cafeteria and the number of students who studied in the student lounge:
60 + 53 = 113
Step 2: Subtract the number of students who studied in both the cafeteria and the student lounge since they have been counted twice in the previous step:
113 - 20 = 93
So, out of the 104 students surveyed, 93 of them studied either in the cafeteria or the student lounge.
To find the number of students who studied only in the cafeteria, we subtract the number of students who studied in both the cafeteria and the student lounge from the total number of students who studied in the cafeteria.
Number of students who studied only in the cafeteria = Total number of students who studied in the cafeteria - Number of students who studied in both the cafeteria and the student lounge
Number of students who studied only in the cafeteria = 60 - 20 = <<60-20=40>>40
To find the number of students who studied only in the student lounge, we subtract the number of students who studied in both the cafeteria and the student lounge from the total number of students who studied in the student lounge.
Number of students who studied only in the student lounge = Total number of students who studied in the student lounge - Number of students who studied in both the cafeteria and the student lounge
Number of students who studied only in the student lounge = 53 - 20 = <<53-20=33>>33
To find the total number of students who studied in either the cafeteria or the student lounge, we add the number of students who studied only in the cafeteria and the number of students who studied only in the student lounge.
Total number of students who studied in either the cafeteria or the student lounge = Number of students who studied only in the cafeteria + Number of students who studied only in the student lounge
Total number of students who studied in either the cafeteria or the student lounge = 40 + 33 = <<40+33=73>>73
Therefore, 73 students studied in either the cafeteria or the student lounge.
To determine the number of students who studied exclusively in each location, we need to subtract the number of students who studied in both locations from the total number of students studying in each location.
1. Number of students who studied exclusively in the cafeteria:
- Total number of students studying in the cafeteria = 60
- Number of students who studied in both the cafeteria and the student lounge = 20
- Number of students who studied exclusively in the cafeteria = Total number of students studying in the cafeteria - Number of students who studied in both locations
= 60 - 20 = 40
2. Number of students who studied exclusively in the student lounge:
- Total number of students studying in the student lounge = 53
- Number of students who studied in both the cafeteria and the student lounge = 20
- Number of students who studied exclusively in the student lounge = Total number of students studying in the student lounge - Number of students who studied in both locations
= 53 - 20 = 33
Therefore, there were 40 students who studied exclusively in the cafeteria, and 33 students who studied exclusively in the student lounge.