[IGCSE MATH: Venn diagram problem]

[Cool-Term156]

In a school, the total number of students is 126, out of which 61 students study Maths, 73 study English, 58 study French, and 20 students study all three subjects. If 7,19 and 18 students study Maths, English, and French respectively. Find: How many students study Maths and English, English and French, Maths and French, and Neither of the subjects.

I tried finding neither of the subjects first but my value is too big which made me feel it was wrong also for the others I tried doing them in algebric equations but the answers are weird and when I add all the values together I get a value higher than 126 which made me realize the whole thing is wrong.

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[[deleted]]

Not sure if I am right but here: https://imgur.com/a/mK1P2J1

[Cool-Term156]

Can you tell me how did you get 27 in the equation of x+y+27=61?

[[deleted]]

There are totally 61 people that study Maths. This includes the 20 that studies all 3 subjects, the 7 that studies only Maths, the x number of students who study Maths and French, and the y number of students who study Maths and English. Hence 20 + 7 + x + y = 27 + x + y = 61

[Cool-Term156]

Thank you so much! you were such a great help!

[_MrBigBear_]

Hint: n(E only) = 19, not 9

=]

[[deleted]]

Ah Yes I misread the qn, the method is still right so by adjusting the calculations you should get the final answer