In a school of 80 students every student studies economics or geography or both.if 65 students study economics and 50 study geography. How many study both subjects?
To find out how many students study both subjects, we can use the principle of inclusion-exclusion.
Let's first find the number of students who study only economics. Since 65 students study economics in total, and we know that some students study both subjects, we subtract the number of students who study both subjects from the total number of students who study economics.
Number of students who study only economics = 65 - x
Similarly, let's find the number of students who study only geography. Since 50 students study geography in total, and we know that some students study both subjects, we subtract the number of students who study both subjects from the total number of students who study geography.
Number of students who study only geography = 50 - x
Now, let's find the total number of students who study both subjects. If we add the number of students who study only economics, the number of students who study only geography, and the number of students who study both subjects, it should add up to the total number of students in the school.
Number of students who study both subjects + Number of students who study only economics + Number of students who study only geography = Total number of students in the school
x + (65 - x) + (50 - x) = 80
Solving this equation, we get:
115 - 3x = 80
-3x = 80 - 115
-3x = -35
x = -35 / -3
x = 35 / 3
Therefore, the number of students who study both subjects is 35/3 or approximately 11.67. However, since we are dealing with a whole number of students, we can only have a whole number of students who study both subjects. Hence, the number of students who study both subjects is 11.