There are 360 people in my school. 15 take calculus, physics, and chemistry, and 15 don't take any of them. 180 take calculus. Twice as many students take chemistry as take physics. 85 take both calculus and chemistry, and 75 take both physics and chemistry. Only 20 take both physics and calculus. How many students take physics?
+128470 See the following Venn Diagram :
The only difficult part is trying to find the number who only take Physics and the number who only take Chemistry
We know that twice as many take Chemistry as take Physics
When we add all the known elements in the diagram we get that 90 students are unaccounted for
If we call x the number who only take Physics....then 90 - x must be the number who only take Chemistry
So we can solve this equation
2 times the number taking Physics = the number taking Chemistry
2 ( 20 + 15 + 75 + x) = 85 + 15 + 75 + ( 90 - x )
2 ( 110 + x ) = 265 - x
220 + 2x = 265 - x
3x = 265 - 220
3x = 45
x =15 = number who only take Physics
90 - 15 =75 = number who only take Chemistry
Number taking Physics = 75 + 15 + 15 + 20 = 125
