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ALGEBRA

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In a recent survey of 100 women, the following information was gathered.
36 use shampoo A.
37 use shampoo B.
38 use shampoo C.
14 use shampoos A and B.
8 use shampoos A and C.
9 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)?

  • ALGEBRA -

    The question is best answered with a Venn diagram.

    Start with those that use all three.
    14 use A & B, so 14-3=11 use A & B but not C.
    8 use A & C, so 8-3=5 use A & C but not C.
    So those who use A only
    A only = 36-(11+3+5)=17

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