Andrew M. answered • 01/28/18

Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors

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.

Andrew M.

01/28/18