Question

A study on how circus ticket pricing influences ticket sales shows that there is an average increase of 4 people for every $3 decrease on the price of the ticket. A circus owner sells an average of 340 tickets when the price of a ticket is $75. If x represents the number of times the price decreases by $3, which function describes the revenue earned by the circus owner in terms of x?
1.-R(x) = 25,800 − 1,020x − 12x2

2.-R(x) = 27,750 − 1,020x − 12x2

3.-R(x) = 25,500 − 720x − 12x2

4.-R(x) = 24,353 − 720x − 12x2

Answer 1

Answer:

3. R(x) = 25,500 -720x -12x²

Explanation:

Starting from 340 tickets, the number of tickets increases by 4 for each unit change in x. Hence, tickets sold will be (340 +4x).

Starting from $75, price per ticket decreases by $3 for each unit change in x. Hence ticket price is (75 -3x).

Revenue from ticket sales is the product of the number of tickets and the price at which they are sold:

... R(x) = (340 +4x)·(75 -3x)

... R(x) = 25,500 -720x -12x² . . . . . matches the 3rd choice