SOLUTION: Hi there, I think this goes here. I have this word problem and I can't seem to wrap my head around it. 300 people attend an interview 100 had mobile phones (x) 70 had Passp

Question 834691: Hi there, I think this goes here.
I have this word problem and I can't seem to wrap my head around it.
300 people attend an interview
100 had mobile phones (x)
70 had Passports (y)
140 had drivers licenses (z)
40 had x+y
30 had y+z
60 had x+z
10 had x+y+z
How many had none?
any help with this would be awesome! Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
A venn diagram really helps you visualize what is going on. So start off by drawing 3 overlapping circles inside a rectangle.

10 had x+y+z (aka 10 had all 3). Keep this in mind for the next parts. This value goes in the very center of the 3 overlapping circles.

60 had x+z. So this means that 60-10 = 50 had only x and z but not y. Notice how we took out the people who had all 3 to make sure of this. This number 50 goes in the region between X and Z (but NOT in any region where Y is overlapping).

Similarly, 30 had y+z, so 30-10 = 20 had only y and z but not x. The number 30 goes in the region between Y and Z (but NOT x). Also, 40 had x+y which means 40-10 = 30 had only x and y but not z. Write the number 40 in the region between X and Y (but not z)

Now we must fill out the rest of the circular regions of the venn diagram. In the x circle for instance, all of the numbers must add to 100 (since there are 100 people who are in region x), so

x + 50 + 10 + 30 = 100

x + 90 = 100

x = 100 - 90

x = 10

The other values are found the same way

y + 30 + 10 + 20 = 70

y + 60 = 70

y = 70 - 60

y = 10

z + 50 + 10 + 20 = 140

z + 80 = 140

z = 140 - 80

z = 60

Finally, we add up all the values in the circular regions (but not outside the 3 circles) to get

10+30+10+50+10+20+60 = 190

This means that there are 190 people who...

a) have just one thing x, y or z

b) have 2 things (x+y, x+z, y+z)

OR

c) have all 3 things (x+y+z)

So there are 300 - 190 = 110 people who have none of these 3 things.

Here is what the venn diagram would look like:

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