A shoe manufacturer markets a new athletic shoe in a community of 500,000 people. The marketing representative convinces 35% of the community to buy the shoe. Additionally, each customer convinces 35% of his or her friends that have not bought the shoe to do so. What total percentage of the population will buy the shoe?

53.8 percent is the answer. Don't question. We are everywhere.

The second part of the question makes no sense.

How are we to know how many friends each member of the first group has?
Two or more members could have the same friends, there would surely be overlap.

To determine the total percentage of the population that will buy the shoe, we need to consider the initial purchases and the subsequent purchases influenced by those customers.

Let's break down the calculation step-by-step:

1. Calculate the number of initial purchases: Multiply the total population by the percentage of people convinced to buy the shoe.
Number of initial purchases = 500,000 * 0.35 = 175,000.

2. Calculate the number of subsequent purchases: For each initial customer, multiply the number of their friends who are convinced to buy the shoe by the percentage of friends persuaded.
Number of subsequent purchases = 175,000 * 0.35 = 61,250.

3. Determine the total number of purchases: Add the initial purchases and the subsequent purchases.
Total number of purchases = 175,000 + 61,250 = 236,250.

4. Calculate the total percentage of the population that will buy the shoe by dividing the total number of purchases by the population size and multiplying by 100.
Total percentage = (236,250 / 500,000) * 100 = 47.25%.

Therefore, the total percentage of the population that will buy the shoe is 47.25%.