1. ## Venn Diagram

I need help with a Venn Diagram question. Oridnarily I know you would start in the middle but that is the piece that is missing in this problem. Can you please provide a formula to work this problem?

A recent survey of 150 people showed the following investments in stocks bonds and CODs

111 people invested in stocks
98 people invested in bonds
100 people invested in CODs
80 people invested in stocks and bonds
83 people invested in bonds and CODs
85 people invested in stocks and CODs
9 people did not invest in any of the three

How many people invested in all three

2. Call the middle intersection X,
and you will the the following picture.
Since the universal set over here is 150,
we add each one and get,
$\displaystyle \begin{array}{c} x-64\\ x-65\\ x-68\\ 80-x\\ 85-x\\ 83-x\\ \underline{x+9}\\ x+60$
Thus,
$\displaystyle x+60=150$
Thus,
$\displaystyle x=90$

3. ## Venn Diagram

Where did you get the
x-64
x-65
x-68?

The total value for stocks should be 111, for bonds 98 and for cods 100. If x was 90 you would be over.

Thanks!

4. Originally Posted by gogo08
Where did you get the
x-64
x-65
x-68?

The total value for stocks should be 111, for bonds 98 and for cods 100. If x was 90 you would be over.

Thanks!
Because those extreme outside circle parts are,
$\displaystyle 111-(x+[80-x]+[85-x])=x-64$

5. Originally Posted by ThePerfectHacker
Because those extreme outside circle parts are,
$\displaystyle 111-(x+[80-x]+[85-x])=x-64$
Hello,

that's what I've got:

$\displaystyle 111-(x+[80-x]+[85-x])=x-54$

That'll give as the final result x = 70 which fits a little bit better because with your result it could happen that -10 people buy bonds and stocks.

Greetings

EB

6. Originally Posted by earboth
Hello,

that's what I've got:

$\displaystyle 111-(x+[80-x]+[85-x])=x-54$

That'll give as the final result x = 70 which fits a little bit better because with your result it could happen that -10 people buy bonds and stocks.

Greetings

EB
I hate these types of mistakes.