Question 1119692: A pizza chain was willing to pay $1 to each person interviewed about his or her likes and dislikes of types of pizza crust. Of the people interviewed, 200 liked thin crust, 270 liked thick crust, 70 liked both, and 50 did not like either type of crust. What was the total cost of the survey?
Answer by ikleyn(52748)   (Show Source):
You can put this solution on YOUR website! .
The total number of interviewed persons was
200 + 270 - 70 + 50 = 450.
So the total cost of the survey was 450 dollars.
The only moment to explain is "what is 200 + 270 - 70 ?".
It is the number of those who likes thin crust OR thick crust.
To calculate it, we simply add 200 and 270 and then subtract 70 of the intersection, whom we counted twice.
See the lesson
- Counting elements in sub-sets of a given finite set
in this site.
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Actually, another interpretation of the condition is possible, too,
by considering 200, 270 and 70 as three NON-INTERSECTING categories.
So, it depends on an interpretation.
UNFORTUNATELY, the problem leaves a gap for such "non-unique" interpretation.
The truly and accurately formulated Math problem should not leave such a gap.
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