Question

A horse-drawn carriage tour company has found that the number of people that take their tour depends on the price charged per customer. The more the company charges for a tour, the fewer people decide to take the tour.

The function c(x)=50+5x represents price charged per customer where x is the number of $5 increases they charge over a rate of $50 per person.


The function p(x)=100−2x represents the number of customers expected for the day, where x is the number of $5 increases they charge over a rate of $50 per person.




What does (p⋅c)(2) mean about the horse-drawn carriage tour company?





The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $40.


The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60. <------- Took the test and this was the right answer.


The horse-drawn carriage tour company can expect to take in $3760 when the charge per customer is $60.


The horse-drawn carriage tour company can expect to take in $3760 when the charge per customer is $40.

Answer 1

b

Explanation:

Answer 2

Option B- The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.

Explanation:

Given :

The function
`c(x)=50+5x` represents price charged per customer where x is the number of $5 increases they charge over a rate of $50 per person.

The function
`p(x)=100-2x` represents the number of customers expected for the day, where x is the number of $5 increases they charge over a rate of $50 per person.

To find : (p⋅c)(2) mean about the horse-drawn carriage tour company.

Solution :

(p.c) means we multiply the p(x) and c(x)

`(p.c)(x)=p(x)* c(x)`

`(p.c)(x)=(100-2x)(50+5x)`

`(p.c)(x)=5000+500x-100x-10x^2`

`(p.c)(x)=5000+400x-10x^2`

Substitute the value of x=2

`(p.c)(2)=5000+400(2)-10(2)^2`

`(p.c)(2)=5000+800-10(4)`

`(p.c)(2)=5800-40`

`(p.c)(2)=5760`

The horse-drawn carriage tour company can expect to take in $5760.

The function
`c(x)=50+5x` represents price charged per customer.

For x=2

`c(x)=50+5(2)`

`c(x)=50+10`

`c(x)=60`

The charge per customer is $60.

Therefore, Option B is correct.

The horse-drawn carriage tour company can expect to take in $5760 when the charge per customer is $60.