Question 1106293
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Let me show you how to solve the problem WITHOUT using a Venn diagram.


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Let B be the number of students who passed the Biology   exam only.

Let C be the number of students who passed the Chemistry exam only.


Then your first equation is  

B + C + 8 = 60      (1)    ("Every student passed at least one of the two subjects and 8 students passed both subjects.")


Your second equation is 

(B+8) - (C+8) = 6   (2)    ("the number of students who passed Biology is 6 more than the number of students who passed Chemistry")



Simplify equations (1) and (2). You will get

B + C = 52,          (1')
B - C =  6.          (2')


Now add equations (1) and (2). You will get

2B = 52 + 6 = 58  ====>  B = {{{58/2}}} = 29.


Then  from (1')  C = 52 - 29 = 23.


<U>Answer</U>.  29 students passed Biology only.

         23 students passed Chemistry only.

         29+8 = 37 passed Biology   (of them, 8 passed both).

         23+8 = 31 passed Chemistry (of them, 8 passed both).
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Solved.