A college survey was taken to determine where students study. Of 120 students surveyed, 84 studied in the ,54 studied in the student union, 24 studied in both the library and the student union.
To determine where students study, we need to find the number of students who study in only the library, the number of students who study in only the student union, and the number of students who study in both the library and the student union.
Let's start by finding the number of students who study in only the library.
To do this, we start with the total number of students surveyed (120) and subtract the number of students who study in both the library and the student union (24) and the number of students who study in only the student union (54).
So, the number of students who study in only the library is 120 - 24 - 54 = 42.
Similarly, let's find the number of students who study in only the student union.
Again, we start with the total number of students surveyed (120) and subtract the number of students who study in both the library and the student union (24) and the number of students who study in only the library (42).
So, the number of students who study in only the student union is 120 - 24 - 42 = 54.
Finally, let's find the number of students who study in both the library and the student union.
This value is already given in the question as 24.
Therefore, we have:
Number of students who study only in the library: 42
Number of students who study only in the student union: 54
Number of students who study in both the library and the student union: 24
To determine the number of students who studied in each location, we can use a Venn diagram.
Let's label the three regions in the Venn diagram as follows:
- A: represents the students who studied in the library
- B: represents the students who studied in the student union
- C: represents the students who studied in both the library and the student union
Given:
- The total number of students surveyed is 120.
- 84 students studied in the library (region A).
- 54 students studied in the student union (region B).
- 24 students studied in both the library and the student union (region C).
Now, we can fill in the information we have in the Venn diagram:
```
_____________
| A |
|___________|
| C
__|___________
| B |
|_____________|
```
To find the number of students who studied only in the library (A - C), we subtract the number of students who studied in both locations (C) from the total number of students who studied in the library (A):
Number of students who studied only in the library = 84 - 24 = 60.
To find the number of students who studied only in the student union (B - C), we subtract the number of students who studied in both locations (C) from the total number of students who studied in the student union (B):
Number of students who studied only in the student union = 54 - 24 = 30.
To find the number of students who studied in either the library or the student union, we add the number of students who studied only in the library (A - C), the number of students who studied only in the student union (B - C), and the number of students who studied in both locations (C):
Number of students who studied in either the library or the student union = (A - C) + (B - C) + C
= 60 + 30 + 24
= 114.
To summarize:
- Number of students who studied only in the library: 60
- Number of students who studied only in the student union: 30
- Number of students who studied in both the library and the student union: 24
- Number of students who studied in either the library or the student union: 114.
To find out how many students studied in the library, we need to subtract the number of students who studied in both the library and the student union from the total number of students who studied at the library.
Given:
Total number of students surveyed = 120
Number of students who studied in the library and the student union = 24
To find the number of students who studied in the library:
1. Subtract the number of students who studied in both the library and the student union from the total number of students who studied at the student union:
54 (students in the student union) - 24 (students in both library and student union) = 30
Therefore, 30 students studied in the library.