Question 1083879
<pre>
{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,x),locate(1.5,1.7,z),locate(-3.7,-1,w), locate(-3.6,2.5,A), locate(-.1,1.8,y),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,B)
 )}}}

  n(A) = 24 = x + y
  n(B) = 17 = y + z
n(AUB) = 32 = x + y + z
 n(A') = 11 = z + w 

So the system of equations is:

(eq. 1)              x + y         = 24
(eq. 2)                  y + z     = 17
(eq. 3)              x + y + z     = 32
(eq. 4)                      z + w = 11

Subtract (eq. 3) minus (eq. 1)

 (eq. 3)              x + y + z     = 32
-(eq. 1)             -x - y         =-24
----------------------------------------
                              z     =  8

Subtract (eq. 3) minus (eq. 2)

 (eq. 3)              x + y + z     = 32
-(eq. 2)                 -y - z     =-17
----------------------------------------
                      x             = 15

Substitute x = 15 in (eq. 1)
(eq. 1)              15 + y         = 24  
                          y         =  9

Substitute z = 8 in (eq. 4)

(eq. 4)                      z + w = 11
                             8 + w = 11
                                 w = 3

{{{drawing(300,200,-4,4,-2,4.8,rectangle(-4,-1.6,4,4.4), locate(-2,1.8,15),locate(1.5,1.7,8),locate(-3.7,-1,3), locate(-3.6,2.5,A), locate(-.1,1.8,9),red(circle(-sqrt(2),sqrt(2),2)),red(circle(-sqrt(2),sqrt(2),1.95)),red(circle(-sqrt(2),sqrt(2),1.975)),
blue(circle(sqrt(2),sqrt(2),2),circle(sqrt(2),sqrt(2),1.95),circle(sqrt(2),sqrt(2),1.975)),
locate(3.4,2.5,B))}}}

Edwin</pre>