Question 635569: In a recent survey of 100 women, the following information was gathered.
38 use shampoo A.
40 use shampoo B.
33 use shampoo C.
4 use shampoos A and B.
11 use shampoos A and C.
13 use shampoos B and C.
3 use all three.
Use the figure to answer the question in the problem.
How many are using shampoo A only (Region I)?
1 . women
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Draw three circles that partially overlap each other; label the circles A, B, and C. In the center, where all three overlap together, put a 3. That accounts for the "3 use all three". Then it says that 4 use A and B, but you already have accounted for 3 of those 4 because of the "3 use all three" statement; if someone uses all three, then they must use A and B, right? So 4 minus 3 is 1, put a 1 in the little segment where only A and B overlap. Similarly, 11 use A and C. Subtract 3 to get 8, and put 8 in the segment where only A and C overlap. Now add up 8 plus 3 plus 1 equals 12 which is the number of people who use A and Something Else (maybe just B, maybe just C, and maybe both B and C). Subtract 12 from the 38 that use A to get 26, the number that use ONLY A.
John
My calculator said it, I believe it, that settles it
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