Venn Diagram help?

Question

After leaving the polls, many people are asked how they voted. (This is called an exit poll.) Concerning Propositions A, B, and C, the following information was obtained: 296 people voted yes on A, 92 voted yes only on A, 343 voted yes on B, 166 voted yes only on B, 517 voted yes on A or B, 332 voted yes on C, no one voted yes on all three, and 73 voted no on all three. (Round your answers to one decimal place.)

 

I'm stuck. I can't figure out how to use this information to fill in the venn diagram I need for the rest of the question. 

Answer 1

Elizabeth... This platform is very difficult to do graphics on.

 

Draw your three overlapping circles A, B, C

In the A only area we have 92

In the B only area we have 166

In the overlap of all 3 circles we have zero

Outside the circles we have 73 who voted no on all 3

 

I labeled the AB overlap as area x

The AC overlap as y

The BC overlap as z

 

From this I used the information to create simultaneous equations

 

296 voted yes on A:

x + y + 92 = 296

x + y = 204   {equation 1}

 

343 voted yes on B:

x + z + 166 = 343

x + z = 177   {equation 2}

 

517 voted yes on A or B:

x + y + z + 258 = 517

x + y + z = 259    {equation 3}

 

In equation 1 solve for y:  y = 204-x

In equation 2 solve for z:  z = 177-x

Substitute those into equation 3

 

x + 204 -x + 177 -x = 259

-x + 381 = 259

-x = -122

x = 122

122 people voted yes to A and B

 

y = 204 - 127

y = 82

82 people voted yes to A and C

 

z = 177 - 122

z = 55

55 people voted yes to B and C

 

A total of 332 voted yes on C:

C + 82 + 55 = 332

C + 137 = 332

C = 332 - 137

C = 195

195 people voted yes to C only

 

All your numbers are there now.  I verified that the totals for each area A, B, C are correct.