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

Answer:

b

Step-by-step explanation:

Answer 2

Answer:

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

Step-by-step 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)

$(p.c)(x)=p(x)\times c(x)$

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

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

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

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.