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Question

A survey recently conducted to find out the number of applicants that applied for jobs in 3 newspaper establishments revealed that 70 applied to newspaper A, 65 applied to newspaper I and 85 applied to newspaper C. 40 applied to ONLY newspaper A, only 20 applied to newspaper I while 45 applied ONLY to newspaper C. If i5 applied to all 3 establishments, find out:

 

(A) the number that applied to BOTH newspapers A and I 

(B) the number that applied to BOTH newspapers A and C

(C) the number that applied to BOTH newspapers C and I

(D) the number that applied to at leas one newspaper establishment.

 

Please help me with this!!!

Answer 1

A Venn diagram will help you visualize this.  A, I, and C

You'll have three overlapping circles with regions where they overlap.

AI, AC, CI, and ACI.

ACI is 15, the number that applied to all three.

 

Just looking at A:

The total for A is 70.

40 applied only to A, so the sum of the overlapping parts is 30, 15 of which applied to all three.

AI+AC+AIC = 30

AI+AC+15 = 30

AI+AC = 15

 

Do the same for C and I to get two more equations.

CI+AC = 40-15 = 25

AI+CI = 45-15 = 30

 

You now have three equations and three unknowns.

AI+AC      = 15

     AC+CI = 25

AI      +CI = 30

 

You can solve this system of equations for the three unknown overlap areas.  Use whatever method your course is teaching: Gaussian or Gauss-Jordan elimination, or one of the matrix algebra methods.

 

Once you have that you can add all of the pieces:

Total applicants = A + B + C + AI + AC + CI + AIC

Where A, B and C are those who applied ONLY to ONE of those newspapers, and AIC is 15.

 

I get this result:

AI = 10

AC = 5

CI = 20

Total = 155

(Don't forget: AIC = 15)

To check, put these numbers in your Venn diagram and add up all the numbers in each circle. (It does check!)