Question 1167409: A survey carried out recently to find the number of applicants that applied for jobs into 3 newspaper establishment, revealed that 70 applied to daily times, 65 applied to Daily graphics and 85 applied to daily punch. 40 applied to daily times only, 20 applied to daily graphics only while 45 applied to daily punch only. If 15 applied to all three newspaper establishment, find:The number that applied to both daily times and daily graphics
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i got the answer, but it wasn't easy and i don't believe it lent itself to any specific formula very well.
this is what i got:
daily times daily graphic daily punch
total 70 65 85
1 only 40 20 45
all 3 15 15 15
1 only + all 3 55 35 60
total - (1 only + all 3) 15 30 25
total - (1 only + all 3) means that each one of those is split between only 1 other, forming 2 only.
so the row with the title of total - (1 only + all 3) can be renamed to 2 only.
the table then looks like this:
daily times daily graphic daily punch
total 70 65 85
1 only 40 20 45
all 3 15 15 15
1 only + all 3 55 35 60
2 only 15 30 25
that 2 only row needs to be split into pairs rather than having entries in all 3 columns.
i had to play around with it until i got what looked like it should be:
the end result was:
daily times daily graphic daily punch
total 70 65 85
1 only 40 20 45
all 3 15 15 15
1 only + all 3 55 35 60
---------------------------------------------------------------------------
daily times daily graphic 10 10
daily times daily punch 5 5
daily graphic daily punch 20 20
---------------------------------------------------------------------------
2 only 15 30 25
the part between the dashed lines is the breakdown of the 2 only row.
your total is the data in the 1 only row and the 3 only row and the 2 only row.
that becomes:
daily times daily graphic daily punch
1 only 40 20 45
all 3 15 15 15
2 only 15 30 25
total 70 65 85
when you break the 2 only row down, then you get:
daily times daily graphic daily punch
1 only 40 20 45
all 3 15 15 15
daily times daily graphic 10 10
daily times daily punch 5 5
daily graphic daily punch 20 20
total 70 65 85
everything checks out.
your solution is that the number that applied to both daily times and daily graphic is 15 that applied to all three plus 10 that applied to daily times and daily graphic only.
therefore, your solution is that the number that applied to daily time and daily graphic is 25.
Answer by ikleyn(52903)  (Show Source):
You can put this solution on YOUR website! .
This problem came to the forum several years ago, and I solved it at that time, see the link
https://www.algebra.com/algebra/homework/sets-and-operations/sets-and-operations.faq.question.1101879.html
For your convenience, I copy-paste and reproduce here that solution again.
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
==========>
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.
INTERMADIATE ANSWER: x= 10; y= 5; z= 20.
FINAL ANSWER: x + 15 = 10 + 15 = 25.
25 applicants applied to BOTH Daily times and Daily graphics.
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