In a class of 50 students, 25 offer mathematics, 22 offer physics, 30 offer chemistry and all the students take at least one of the subjects. 10 offer physics and mathematics, 8 offer chemistry and mathematics, 16 offer physics and chemistry.

Question

1. Draw a Venn diagram to illustrate the information.
2. Find the number of students who offer all the three subjects.

Answer 1

Instead of "offer," do you mean "take or study"?

Answer 2

Place x in the intersection of all 3 circles
Now look at the intersection of Math and Physics
It says 10 take Math and Physics, but you already have x marked in there.
So put 10-x is the open part of that intersection.
Proceed in the same way for the other two double intersections.
Now look at the math circle.
We already have marked x and 10-x, and we are told that 25 take math
so the part of only math = 25 - x - (10-x) = 7-x
Do the same for the other circles

All the regions should now be marked, but you know they must total 50.
So ......
add them up, then set that sum equal to 50 , solve for x

Answer 3

https://www.jiskha.com/questions/1797301/In-a-class-of-43-students-at-least-every-one-of-them-offers-physics-or-geography

Wherever the textbook comes from, the identical error in English vocabulary has been showing up whenever a student posts this question. It's a shame that students are having to use faulty texts like this. =(