Robert Z. answered • 09/15/20

3100+ hours (& counting!) tutoring math -- Prealgebra to Calculus 2

Krugen K.

asked • 05/27/20Q. In a survey conducted for three perfumes, it was found that 40% of the respondents used Fa, 25 % used Havoc, and 60 % used **B**yredo. 16% used none of the three perfumes, whereas 15% of the respondents used exactly two of the three perfumes.

- What percentage of the respondents used all three perfumes?
- What percentage of the respondents used at least two perfumes?
- It is found that 22% of the respondents used both Havoc and Byredo. What percentage of the respondents used only Fa?

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Robert Z. answered • 09/15/20

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3100+ hours (& counting!) tutoring math -- Prealgebra to Calculus 2

Label perfumes A, H, B

Let AcHcBc = S1, AHcBc = S2, AcHBc = S3, AcHcB = S4, AHBc = S5, AHcB = S6, AcHB = S7, and AHB = S8

1)S1 + S2 + S3 + S4 + S5 + S6 + S7 + S8 = 1

2)S1 = .16

3)S2 + S5 + S6 + S8 = .4

4)S3 + S5 + S7 + S8 = .25

5)S4 + S6 + S7 + S8 = .6

6)S5 + S6 + S7 = .15

1 From the first two equations, 7) S2+S3+S4+S5+S6+S7+S8 = .84

If we add equations, 3, 4, and 5, and subtract 6 and 7, we get

2 S8 = .4 + .25 + .6 - .15 - .84

2S8 = .26

S8 = .13. Let's call this 8)

2 At least 2 equals exactly 2 or 3 = .15 + .13 = .28

3 If 22% used Havoc and Breedo, then 9) S7 + S8 = .22

Then, as 2) S2 + S5 + S6 + S8 = .4

6) S5 + S6 + S7 = .15

8) S8 = .13

9) S7 + S8 = .22

Equation 2 - Equation 6 + Equation 9 - 2 * Equation 7 gives you

S2 = .4 - .15 + .22 - 2 * .13

S2 = .21

Krugen K.

Thank you.
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06/03/20

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Krugen K.

Oh you answered it, I never checked back, thank you so much, this is a way better method.03/28/21