SOLUTION: A company is considering manufacturing a new product that has two different flavors, orange and cherry. They surveyed 150 people. The results are as follows. 75 liked cherry 94

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Question 206978: A company is considering manufacturing a new product that has two different flavors, orange and cherry. They surveyed 150 people. The results are as follows.
75 liked cherry
94 liked orange
22 like both flavors
Construct a Venn diagram and answer the following:
a) how many liked only orange flavor?
b) how many liked only cherry flavor?
c) how many liked either one or the other or both?
d) how many liked neither?
Answer by mickclns(59) About Me  (Show Source):
You can put this solution on YOUR website!
+drawing%28200%2C200%2C0%2C200%2C0%2C200%2C%0D%0A+++++circle%2875%2C100%2C70%29%2C%0D%0A+++++circle%28125%2C100%2C70%29%2C%0D%0A%0D%0A+++++locate%2830%2C175%2CO%29%2C%0D%0A+++++locate%28165%2C175%2CC%29%2C%0D%0A%0D%0A+++++rectangle%281%2C199%2C199%2C1%29%0D%0A%29+
 
There are 4 separate (mutually exclusive) regions in this diagram: 1) the part inside both circles (their intersection), 2) The part inside O but not inside C, 3) the part inside C but not inside O 4) The part outside both O and C.
Since 22 like both flavors, that number goes in the intersection of O and C.
Since 75 like Cherry, and 22 like both, 75-22=53 like Cherry but not Orange.
Since 94 like Orange, and 22 like both, 94-22=72 like Orange but not Cherry.
+drawing%28200%2C200%2C0%2C200%2C0%2C200%2C%0D%0A+++++circle%2875%2C100%2C70%29%2C%0D%0A+++++circle%28125%2C100%2C70%29%2C%0D%0A%0D%0A+++++locate%2830%2C175%2CO%29%2C%0D%0A+++++locate%28165%2C175%2CC%29%2C%0D%0A%0D%0A+++++rectangle%281%2C199%2C199%2C1%29%2C+%0D%0A%0D%0A+++++locate%2889.5%2C110%2C+22%29%2C%0D%0A+++++locate%28155%2C110%2C+53%29%2C%0D%0A+++++locate%2833%2C110%2C+72%29%2C%0D%0A+++++locate%2820%2C30%2C+3%29%0D%0A%29+
Together the 4 sections include 150 people and the 3 sections so far filled include 22+53+72=147 people, so 150 - 147 = 3 people like neither Orange nor Cherry.
 
The answers to the questions:
a) how many liked only orange flavor? *** 72
b) how many liked only cherry flavor? *** 53
c) how many liked either one or the other or both? *** 147
d) how many liked neither? *** 3