Question 1138772: Q10. A performer charges C(x) = 50x + 10,000, where x is the total number of attendees at a show. The venue charges $75 per ticket. After how many people buy tickets does the venue break even, and what is the value of the total tickets sold R(x) at that point?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the cost to the people who are renting the location of the show is equal to c(x).
c(x) is equal to 50 * x + 10,000.
x is the total number of people who attend the show.
the cost to the people who attend the show is 75 dollars per person.
the revenue to the people who are renting the location is therefore r(x) = 75 * x.
the show breaks even when the cost to rent the location of the show is equal to the revenue from the people who attend the show.
you get c(x) = r(x).
since c(x) = 50 * x + 10,000 and r(x) is equal to 75 * x, you get:
50 * x + 10,000 = 75 * x
subtract 50 * x from both sides of this equation to get:
10,000 = 75 * x - 50 * x
combine like terms to get 10,000 = 25 * x.
solve for x to get x = 10,000 / 25 = 400.
the show will break even when 400 tickets are sold.
c(400) becomes 50 * 400 + 10,000 = 30,000.
r(400) becomes 75 * 400 = 30,000
the cost is equal to the revenue, so the break even point is when 400 tickets are sold.
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