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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?

 Jan 26, 2021
 #1
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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

 

 

cool cool cool

 Jan 26, 2021

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