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 $3760 when the charge per customer is $60.

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

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

Answer 1

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

(p * c) (2) =
(100-2*2) (50+5*2)
(96) (60)
=5760

Answer is B.

Answer 2

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

Explanation:

We have,

The function representing the price charged by the customers is
`c(x)=50+5x`.

The function representing the number of customers is
`p(x)=100-2x`.

Then, the product of the functions is given by,

`(p* c)(x)=p(x)* c(x)\\\\(p* c)(x)=(100-2x)(50+5x)\\\\(p* c)(x)=-10x^2+400x+5000`

Substituting x = 2 in the above product gives,

`(p* c)(2)=-10* 2^2+400* 2+5000\\\\(p* c)(2)=-40+800+5000\\\\(p* c)(2)=\$ 5760`

Also, the charge per customer when x = 2 is,

`c(x)=50+5x\\\\c(x)=50+5* 2\\\\c(x)=50+10\\\\c(x)=\$ 60`

Hence, the product (p-c)(2) represents,

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