A study on how circus ticket pricing influences ticket sales shows that there is an average increase of 4 people for every $3 de crease 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 answer:
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
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