Question 1118566: For an upcoming event, a 2500 seat arena is selling tickets for $25 and $15. At least 1000 tickets must be priced at $15 and total sales need to exceed $10,000 to make a profit. Let x represent the number of tickets priced at $25 and y represent the number of tickets priced at $15. Write a system of inequalities that shows the possible combinations of ticket sales in order to make a profit.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! number of seats is 2500 which means that a total of 2500 tickets can be sold.
let x equal the number of tickets sold at 25 dollars.
let y equal the number of tickets sold at 15 dollars.
25x equals the amount of money made from selling 25 dollar tickets.
15y equals the amount of money made from selling 15 dollar tickets.
total sales must be greater than 10,000, so 25x + 15y >= 10,000.
maximum number of tickets that could be sold is 2500, so x + y <= 2500.
at least 1000 tickets must be priced at 15 dollars, so y >= 1000.
your system of requirements would be:
y >= 1000
25x + 15y >= 10,000
x >= 0 (unstated but necessary since number of tickets can't be negative).
x + y <= 2500
note that, if you only sold 1000 tickets at 15 dollars apiece, you would automatically make a profit because 15 * 1000 = 15,000 which is greater than 10,000.
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