Question 1207374
<pre>

If you know how to use EXCEL to solve a system of equations 
or if you have a system solver on your calculator, you can 
use this method:
 
{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"a=?"),
locate(-3.5,-2,"h=?"),
locate(0,-2.7,M),
locate(-.45,-1,"g=?"),
locate(.6,.4,"f=?"),
circle(sqrt(2),sqrt(2),2),
locate(-3.5,2.5,L),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,U),
locate(-1.5,.5,"d=?"),
locate(-.4,2.3,"b=?"),
locate(1.8,2,"c=?"),
locate(-.4,1.1,"e=?") )}}}

A survey of 1,174 tourists visiting Orlando was taken. 

So a+b+c+d+e+f+g+h=1174

250 tourists had visited LEGOLAND

So a+b+d+e=250

268 tourists had visited Universal Studios

So b+c+e+f=268

53 tourists had visited both the Magic Kingdom and LEGOLAND

So d+e=53

100 tourists had visited both the Magic Kingdom and Universal Studios

So e+f=100

77 tourists had visited both LEGOLAND and Universal Studios

So b+e=77

32 tourists had visited all three theme parks

So e=32

79 tourists did not visit any of these theme parks

So h=79

How many tourists only visited the Magic Kingdom (of these three)?

{{{system(a+b+c+d+e+f+g+h=1174,a+b+d+e=250, b+c+e+f=268, d+e=53, e+f=100,  b+e=77, e=32,  h=79)}}}

Solve the system.

{{{drawing(300,300,-4,4,-5,4,
rectangle(-4,-3.5,4,4),
circle(0,-.5,2),
locate(-2.3,2,"a=152"),
locate(-3.5,-2,"h=79"),
locate(0,-2.7,M),
locate(-.45,-1,"g=654"),
locate(.6,.4,"f=68"),
circle(sqrt(2),sqrt(2),2),
locate(-3.5,2.5,L),
circle(-sqrt(2),sqrt(2),2),
locate(3.5,2.5,U),
locate(-1.5,.5,"d=21"),
locate(-.4,2.3,"b=45"),
locate(1.8,2,"c=123"),
locate(-.4,1.1,"e=32") )}}}

Edwin</pre>