Amy S.

asked • 01/19/18

Easy but I don't understand! Sets, Venn diagrams

In the figure ξ is the set of all students in Secondary One. (The figure shows a Venn diagram with two overlapping circles. There is only 1 intersection, labeled y. The left circle is represents G and the right circle represents C. circle G, without the intersection is part x and circle C without the intersection is part z. the letter w is outside the Venn diagram but within the box.)

G= {students who joined uniformed groups} and 
C= {students who join clubs and societies},
 
The letters w, x, y, and z in the figure, represent the number of students in each subset. Given that n(ξ)= 200, n(G)= 120, and n(C)= 90,
 
a) find the smallest possible value of y
 
b) find the largest possible value of w 
 
c) find the value of x and z if w=30
 
 
 
i need step by step answers for both parts! Thanks in advance. It is quite a simple question but I dont understand how to do both parts. Can't the smallest possible value of y be a zero?

2 Answers By Expert Tutors

By:

David W. answered • 01/19/18

Experienced Prof

Amy S.

I forgot to add, but there is a part c) which is to find the value of x and z if w=30. Could you help me with this part too? Thanks a lot!
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01/19/18

David W.

tutor
Well, w  = y - 10
       w=30
       y=30
Then, x + y = 120 ;  x+30 = 120;  so, what is x?
       z + y = 90 ;  z+30=90;  so, what is z?
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01/19/18

David W.

tutor
Let's try that again.
 
Well, y = w + 10       [see part (b)]
        y = 30 + 10
        y = 40
Then, x+y = 120;    x+40=120; so what is x?
         z+y = 90;    z+40=90;   so, what is z?
 
Check:    Is    w + x + y + z = 200   ?
                   30 + 80 + 40 + 50 = 200    ?
                         200 = 200   ?yes                    
      
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01/19/18

Amy S.

How did you know that w = y - 10? I don't get that portion
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01/19/18

Amy S.

Wait apologies, ignore the above comment oops! the answer I got was x=80 and z= 50
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01/19/18

David W.

tutor
Great !!
 
As you can see from my "Check," that's what I got also.
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01/19/18

Lori C. answered • 01/19/18

Algebra, Trigonometry and Calculus

Amy S.

Yes it helps. Thanks a lot for the detialed explanation. 5 stars! :))
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01/19/18

Lori C.

You're very welcome!
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01/19/18

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