# Venn diagram problem

How many in only single?

3 Magazines (D, R, I); total number of people is 1000

250 - D, I, not R

40 - I, R, not D

120 - R, not in I

200 - I, not in D

90 - D, R

70 - none

This is a review but I don't understand

Professor told us to get answer = (y+Z+160)+250+90-x+X=40+70=1000

But I don't understand how to get y, z and x?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Hi,

Please find the solutions/explanations attached.

How many in only single?

3 Magazines (D, R, I); total number of people is 1000

250 - D, I, not R

40 - I, R, not D

120 - R, not in I

200 - I, not in D

90 - D, R

70 - none

There will be 160 in only I as given 200 - I, not in D.

We know that total is 1000 (using Venn diagram).

Total sum is 1000.(add up all)

x + y + 90 - y + 250 + 40 + 160 + z + 70 = 1000

x + z + 540 = 1000

x + z = 1000 - 610 = 390

In single there will be x + z + 160 = 390 + 160 = 550

https://brainmass.com/math/discrete-math/venn-diagram-problem-246283