Question 1101879: A survey carried out recently to find the number of applicants that applied for jobs in three newspaper establishments, revealed that 70 applied to the Daily Times,65 applied to the Daily Graphic, and 85 applied to the punch. 40 applied to the Daily Times only,20 applied to the Daily graphic only, while 45 applied to the punch only. If 15 applied to all the three newspaper establishments find
i. The number that applied to both the Daily Times and the Daily graphics
ii. The number that applied to the Daily Times and the punch
iii.the number that applied to both the Daily graphics and the punch
iv.the number that applied to atleast one newspaper establishments.....please I need details on this it's contradicting my own solving
Found 2 solutions by ikleyn, richwmiller:
Answer by ikleyn(52780)   (Show Source):
You can put this solution on YOUR website! .
Given: DT (marked "T"), 70 & 40 (red circle).
DG (marked "G"), 65 & 20 (green circle).
P, 85 & 45 (blue circle).
Venn diagram
Given: T (70 & 40), G (65 & 20) and P (85 & 45).
Unknowns: x, y, and z.
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Solution
x + y + 15 + 40 = 70
y + z + 15 + 45 = 85
x + z + 15 + 20 = 65
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x + y = 15, (1)
y + z = 25, (2)
x + z = 30. (3)
------------------------Add 3 equations ====>
2x + 2y + 2z = 15 + 25 + 30 = 70 ====>
x + y + z = 35. (4)
Subtract (1) from (4): z= 20;
Subtract (2) from (4): x= 10;
Subtract (3) from (4): y= 5.
Answer: x= 10; y= 5; z= 20.
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Answer by richwmiller(17219)  (Show Source):
You can put this solution on YOUR website! Initial Venn Diagram with given info
Final completed Venn Diagram with calculated info
The other tutor's answers are incomplete, perhaps deliberately so.
i. The number that applied to both the Daily Times and the Daily graphics
abc(15) +ab(5)=20
ii. The number that applied to the Daily Times and the punch
abc(15)+ac(10)=25
iii.The number that applied to both the Daily graphics and the punch
abc(15) +bc(20)=35
iv.The number that applied to at least one newspaper establishments.
Total applications add up all parts
a+b+c+ab+bc+ac+abc+o"
40+45+20+5+20+10+15+0=155
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