In a recent survey of 100 women, the following information was gathered.

29 use shampoo A.
28 use shampoo B.
34 use shampoo C.
3 use shampoos A and B.
7 use shampoos A and C.
6 use shampoos B and C.
1 use all three.
How many use shampoo A only?

See Related Questions below.

29 - 3 - 7 + 1 = 20

To find out how many respondents use shampoo A only, we need to analyze the given information and consider the principles of set theory.

Let's break down the information we have:

- 29 respondents use shampoo A.
- 3 respondents use both shampoo A and B.
- 7 respondents use both shampoo A and C.
- 1 respondent uses all three shampoos.

From this information, we can calculate the number of respondents who use shampoo A only by subtracting the number of respondents who use both shampoo A and either B or C, as well as those who use all three shampoos, from the total number of respondents who use shampoo A.

Here's the step-by-step calculation:

Total respondents using shampoo A = 29

Respondents using both shampoo A and B = 3

Respondents using both shampoo A and C = 7

Respondents using all three shampoos = 1

Total respondents using at least two shampoos = Respondents using both shampoo A and B + Respondents using both shampoo A and C - Respondents using all three shampoos
= 3 + 7 - 1
= 9

Respondents using shampoo A only = Total respondents using shampoo A - Total respondents using at least two shampoos
= 29 - 9
= 20

Therefore, 20 respondents use shampoo A only.