Question 1175375
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There are numerous ways to set up this problem for solving.  I will only show the method I would prefer to use.  Probably other tutors will provide responses showing different methods.<br>
You can look at the different methods and find one that "works" for you.<br>
Basically, I prefer to set the problem up so that it can be solved using ratios, instead of fractions.<br>
"60% of the students who study physics also study chemistry"<br>
means<br>
"3/5 of the students who study physics also study chemistry"<br>
which means<br>
The ratio of the number of students who take both subjects to the number who take only physics is 3:2.<br>
NOTE: being able to convert the given fraction 3/5 into the ratio 3:2 is a useful skill that can often lead to easier ways to solve problems.<br>
Given that 3:2 ratio....<br>
let 3x be the number who take both subjects
let 2x be the number who take only physics<br>
Similar reasoning tells us that "...one third of the chemistry students study physics" means that the number of students who study chemistry only is twice the number who take both subjects.  (The given fraction 1/3 was converted to the ratio 1:2.)<br>
We have 3x as the number who study both subjects, so the number who study chemistry only is 6x.<br>
All students take one subject of the other, or both.  So the sum of the numbers who take physics only, chemistry only, or both must equal the total number of students:<br>
2x+3x+6x = 110
11x = 110
x = 110/11 = 10<br>
ANSWER: The number of students who study both subjects is 3x = 30.<br>
(and 20 take physics only, and 60 take chemistry only....)<br>