A survey was taken at Small Liberal U (SLU) with the followingresult:
235 Total number of students
85 Number of students enrolled in an English class
60 Number of students enrolled in a social studies class
85 Number of students enrolled in a math class
35 Number of students enrolled in both an English class and a math class
30 Number of students enrolled in both an English class and a social studies class
20 Number of students enrolled in both social studies class and a math class
10 Number of students enrolled in all three
a. Complete the Venn diagram to represent information provided.
b. How many students are enrolled in only one class (not two or three)?
There are 150 students who are enrolled in only one class.
To calculate this, we add up the numbers of students in each individual category:
- 85 in English class only
- 60 in social studies class only
- 85 in math class only
Then we subtract the number of students who are enrolled in two or three classes:
- 35 in both English and math
- 30 in both English and social studies
- 20 in both social studies and math
- 10 in all three classes
So, 85 + 60 + 85 - 35 - 30 - 20 - 10 = 150.
To complete the Venn diagram, we need to represent the information provided. First, draw three overlapping circles to represent the three classes: English, Social Studies, and Math.
Next, fill in the information provided:
- In the English circle, write 85 (the number of students enrolled in an English class).
- In the Social Studies circle, write 60 (the number of students enrolled in a social studies class).
- In the Math circle, write 85 (the number of students enrolled in a math class).
- In the overlapping region between English and Math, write 35 (the number of students enrolled in both an English class and a math class).
- In the overlapping region between English and Social Studies, write 30 (the number of students enrolled in both an English class and a social studies class).
- In the overlapping region between Social Studies and Math, write 20 (the number of students enrolled in both a social studies class and a math class).
- Finally, in the very center where all three circles overlap, write 10 (the number of students enrolled in all three classes).
The completed Venn diagram should now accurately represent the information provided.