Question 715243: Draw a Venn diagram representing this survey and label the areas.
In a survey of the dining preferences of 110 students, the following facts were discovered about Adam's Sandwiches(A), the Pizza House (P), and the Dining Hall (D)
30 liked A but not P
21 liked only A
63 liked A
58 liked P
27 liked D
25 liked p and A, but not P
18 liked p and D
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I know you have typos because there is lowercase p along with capital P,
and the second to the last statement ("25 liked p and A, but not P") does not make sense.
Here is what I think you meant:
30 liked A but not P
21 liked only A
63 liked A
58 liked P
27 liked D
25 liked P and A, but not D
18 liked P and D
I would start with a diagram that covers all the possibilities, and start filling numbers in the various regions, even if one or more of them get a zero.
 21 liked only A, and 30 liked A but not P 
Now we think about the students who liked A and also P, in theose two regions in the middle of the diagram. Of the 60 who like A, 30 do not like P, so 63-30=33 like A and P.
Some of those 33 may like A and P only, but maybe some like all three places.
25 like P and A, but not D, so 33-25=8 like all three.  18 liked P and D, so 
Now we just need to find how many like only P,
and how many like only D.
Of the 58 who like P 25+8+10=43 also like at least one other place.
That leaves 58-43=15 who like only P.
Of the 27 who like D, 9+8+10=27 also like at least one other place.
That means that the number of students who like only D, and no other place is 27-27=0.
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