A college survey was taken to determine where students study. Of 114 students surveyed, 73 studied in the cafeteria, 55 studied in the student union, 21 studied in both the cafeteria and the student union.
Of those interviewed how many did not study in either the cafeteria or the student union?
__
To find the number of students who did not study in either the cafeteria or the student union, we can subtract the number of students who studied in either one or both locations from the total number of students surveyed.
First, we add the number of students who studied in the cafeteria (73) and the number of students who studied in the student union (55). However, since 21 students studied in both locations, we have to subtract this number once to avoid counting them twice.
73 + 55 - 21 = 107
So, 107 students studied in either the cafeteria or the student union.
Now, we subtract this from the total number of students surveyed to find those who did not study in either location.
114 - 107 = 7
Therefore, 7 students did not study in either the cafeteria or the student union.
To find out how many students did not study in either the cafeteria or the student union, we need to subtract the number of students who studied in either location from the total number of students interviewed.
Total number of students interviewed = 114
Number of students who studied in the cafeteria = 73
Number of students who studied in the student union = 55
Number of students who studied in both the cafeteria and the student union = 21
To calculate the number of students who did not study in either location, we can use the principle of inclusion-exclusion:
Number of students who did not study in either the cafeteria or the student union = Total number of students interviewed - (Number of students who studied in the cafeteria + Number of students who studied in the student union - Number of students who studied in both the cafeteria and the student union)
Number of students who did not study in either the cafeteria or the student union = 114 - (73 + 55 - 21)
Simplifying the expression:
Number of students who did not study in either the cafeteria or the student union = 114 - (128 - 21)
Number of students who did not study in either the cafeteria or the student union = 114 - 107
Therefore, the number of students who did not study in either the cafeteria or the student union is 7.
To find out how many students did not study in either the cafeteria or the student union, we need to consider the total number of students surveyed and subtract the number of students who studied in either the cafeteria or the student union.
The first step is to add the number of students who studied in the cafeteria (73) and the students who studied in the student union (55). This will give us the total number of students who studied in either location, but we have to be careful not to double-count the students who studied in both places.
So, we subtract the number of students who studied in both the cafeteria and the student union (21) from the sum of students who studied in the cafeteria and the student union:
73 (studied in the cafeteria) + 55 (studied in the student union) - 21 (studied in both) = 107
Therefore, out of the 114 students surveyed, 107 studied in either the cafeteria or the student union. To find the number of students who did not study in either of these locations, we subtract 107 from the total number of students surveyed:
114 (total students) - 107 (studied in either location) = 7
Therefore, 7 students did not study in either the cafeteria or the student union.