Question

three girl scouts are selling cookies in the same neighborhood. 30% buy from alice, 55% from barbara, and 40% from carol. no one who buys from alice also buys from barbara or carol. 10% of the neighbors do not buy any cookies at all. what percent of the neighbors buy from both barbara and carol?

Answer 1

To determine the percentage of the neighbors who buy from both Barbara and Carol, we calculate the overlap by subtracting the sum of Alice's customers and those who buy from no one from the total percentage. The overlap is 35%, which represents those neighbors buying from both Barbara and Carol.

Step-by-step explanation:

To find the percent of neighbors who buy from both Barbara and Carol, we need to consider that no one who buys from Alice buys from the other two, and that 10% do not buy at all. Since the percentages for Barbara and Carol add up to more than 100% when combined (55% + 40% = 95%), and we know that 30% buy only from Alice and 10% buy from no one, there is an overlap between Barbara and Carol.

First, let's subtract the percentages of Alice's customers and those who buy from no one from 100%:

100% - 30% (Alice's customers) - 10% (no buyers) = 60%

This 60% represents the total market share of Barbara and Carol combined, without overlaps. However, since 95% of the neighbors buy from Barbara or Carol individually, we need to find the overlap:

95% (Barbara's + Carol's individual shares) - 60% (combined market without overlaps) = 35%

Therefore, 35% of the neighbors buy cookies from both Barbara and Carol.