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?

Answer 1

Let the price of a ticket be originally T dollars, and the number of clients be N.

let the price decrease by x  3-dollars.

"there is an average increase of 4 people for every $3 decrease on the price of the ticket."

means:

if the price is decreased by 1-3$:
 then N become N+4, and T becomes T-3    


if the price is decreased by 2-3$:
 then N become N+4+4=N+2*4, and T becomes T-3-3=T-2*3    

 So if the price is decrease by x-3 dollars:

N  becomes N+4x, and T becomes T-3x


"A circus owner sells an average of 340 tickets when the price of a ticket is $75."

In this case N=340, and T=75$

If the owner does not change the price ticket, x=0, the revenue is 340*75,

If the owner decreases the price of the tickets by x-3$, then the revenue will be 
(N+4x)(T-3x)=(340+4x)(75-3x) dollars,

If R is the function of the revenue depending on x, then 

R(x)=(340+4x)(75-3x) dollars

 
Answer: R(x)=(340+4x)(75-3x) dollars