SOLUTION: A survey of 300 parks showed the following: 15 had only camping 20 had only hiking trails 35 had only picnicking 185 had camping 140 had camping and hiking trails

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Question 1164091: A survey of 300 parks showed the following:
15 had only camping
20 had only hiking trails
35 had only picnicking
185 had camping
140 had camping and hiking trails
125 had camping and picnicking
210 had hiking trails
Determine the number of parks that:
had at least one of these features
had all three features
did not have any of these features
had exactly two of these features
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
15 had only camping
a = 15
20 had only hiking trails
d = 20
35 had only picnicking
i = 35
185 had camping
 a+b+e+f = 185
15+b+e+f = 185
   b+e+f = 170
140 had camping and hiking trails
     b+f = 140

   b+e+f = 170
   b  +f = 140
     e   =  30
125 had camping and picnicking
     e+f = 125
    30+f = 125
       f =  95

     b+f = 140
    b+95 = 140
       b =  45
210 had hiking trails
   b+d+f+g = 210
45+20+95+g = 210
     160+g = 210
         g = 50
...300 parks...
       a+b+d+e+f+g+i+j = 300
15+45+20+30+95+50+35+j = 300  
                 290+j = 300
                     j =  10
Determine the number of parks that:
had at least one of these features

All but j, 300-10 = 290
had all three features
f=95
did not have any of these features
j=10
had exactly two of these features
b+e+g = 45+30+50 = 125

Edwin