Answer:
517
Step-by-step explanation:
We can draw a Venn diagram to represent the data.
First, identify the groups.
- Let E = students who study English
- Let M = students who study Math
- Let S = students who study Science
Then draw the Venn diagram to represent the groups.
Given 73 students study all subjects:
E ∩ M ∩ S = 73 (add this to the middle section)
Next, add the numbers for the sections where the students study 2 topics.
E ∩ M but not S: 152 - 73 = 79
M ∩ S but not E: 79 - 73 = 6
S ∩ E but not M: 139 - 73 = 66
Now complete each circle by making sure that the values add up to the total value given.
Only E = 254 - S ∩ E - E ∩ M - E ∩ M ∩ S = 254 - 66 - 79 - 73 = 36
Only M = 280 - E ∩ M - M ∩ S - E ∩ M ∩ S = 280 - 79 - 6 - 73 = 122
Only S = 280 - M ∩ S - S ∩ E - E ∩ M ∩ S = 280 - 6 - 66 - 73 = 135
To find the total number of students in the school, add the numbers in each section of the Venn diagram:
73 + 79 + 6 + 66 + 36 + 122 + 135 = 517
