Question

Audrianna gives a walking tour of a popular tourist city to one person for $ 49. To increase her​ business, she would lower the price by​ $2 per person for each additional person. Write the cost per person c as a function of the number of people n on the tour. How much does she make for a tour with 19 ​people?

Answer 1

The cost per person can be expressed as a function of the number of people on the tour. Audrianna would make $13 for a tour with 19 people.

Step-by-step explanation:

The cost per person c can be expressed as a function of the number of people n on the tour as follows:

If Audrianna is giving a tour to one person, the cost would be $49.

If there are additional people on the tour, the price per person would be $2 less than the previous person. So, if there are 2 people on the tour, the cost would be $49 - $2 = $47 per person.

Using this pattern, we can write the function as:

c(n) = 49 - 2(n - 1)

To find out how much Audrianna makes for a tour with 19 people, we plug in 19 for n in the function:

c(19) = 49 - 2(19 - 1) = 49 - 2(18) = 49 - 36 = $13

Answer 2

The price for one person is $ 49. For every extra person, Audrianna lowers the price by $ 2. Thus, it is necessary to create a function where cost (C) will vary according to the variation in the number of people (N).

For more than one person, we must put variable C as a function of the variation in the number of people. However, we want to find the price. To find the price for each extra person, simply decrease the one-person value ($ 49) of the discount ($ 2) multiplied by the total number of people (N).

Thus, we have the following function: C = 49 - 2(N)

For one more person: C = 49 - 2 (1) = $ 47

For two more people: C = 49 -2 (2) = $ 45

(...)

For nineteen more people: C = 49 -2 (19) = $ 11

So if nineteen people participate in the tour, the cost for each person will be $ 11.