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?

Guest Jan 26, 2021

#1**+1 **

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

CPhill Jan 26, 2021