In a class of 80 students, every student had to study Economics or Geography or both Economics and Geography. lf 65 students studied Economics and 50 studie...
Question 1 Report
In a class of 80 students, every student had to study Economics or Geography or both Economics and Geography. lf 65 students studied Economics and 50 studied Geography, how many studied both subjects?
Answer Details
We are given that every student had to study Economics or Geography or both. Therefore, the total number of students in the class is 80.
Let's denote the number of students who studied only Economics by 'E', the number of students who studied only Geography by 'G', and the number of students who studied both subjects by 'B'. Then we can use a Venn diagram to represent the information given in the problem:
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| Economics | Geography |
| | |
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| |
| |
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B G
| |
| |
| |
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| | |
| Only Economics | Only Geography |
| | |
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We are given that 65 students studied Economics, which includes both those who studied only Economics and those who studied both subjects. So we can write:
E + B = 65
Similarly, we are given that 50 students studied Geography, which includes both those who studied only Geography and those who studied both subjects. So we can write:
G + B = 50
We want to find the value of B, the number of students who studied both subjects. To do this, we can add the two equations above:
E + B = 65
G + B = 50
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E + G + 2B = 115
We know that the total number of students in the class is 80, so we can write:
E + G + B = 80
Substituting the expression for E + G + 2B into this equation, we get:
115 - B = 80
Solving for B, we get:
B = 35
Therefore, 35 students studied both Economics and Geography.
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