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.

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changkyun changkyun · Answer 1 · 2018-03-09T21:28:27+01:00

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

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

Answer is B.

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wagonbelleville wagonbelleville · Answer 2 · 2019-03-29T09:10:41+01:00

Answer:

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

Step-by-step explanation:

We have,

The function representing the price charged by the customers is [tex]c(x)=50+5x[/tex].

The function representing the number of customers is [tex]p(x)=100-2x[/tex].

Then, the product of the functions is given by,

[tex](p\times c)(x)=p(x)\times c(x)\\\\(p\times c)(x)=(100-2x)(50+5x)\\\\(p\times c)(x)=-10x^2+400x+5000[/tex]

Substituting x = 2 in the above product gives,

[tex](p\times c)(2)=-10\times 2^2+400\times 2+5000\\\\(p\times c)(2)=-40+800+5000\\\\(p\times c)(2)=\$ 5760[/tex]

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

[tex]c(x)=50+5x\\\\c(x)=50+5\times 2\\\\c(x)=50+10\\\\c(x)=\$ 60[/tex]

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.