Correct answer only ! 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)=80−2x 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?

(A) $4560 when customer is charged $60

Step-by-step explanation:

p(x) = 80 - 2x    where p(x) represents the number of customers

c(x) = 50 + 5x    where c(x) represents the price charged to customers

x represents the number of $5 increases to the $50 charge

(p · c)(x) = (80 - 2x)(50 + 5x)

             = 80(50 + 5x) -2x(50 + 5x)

             = 4000 + 400x - 100x - 10x²

             = 4000 + 300x - 10x²

(p · c)(2) = 4000 + 300(2) - 10(2)²  

             = 4000 + 600 - 40

             = 4560

the company will receive $4560 when 2($5) is added to the $50 charge        

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