Question

The opera house sells an average of 1700 tickets per night when the price of each ticket is 25$ an employee of the opera house noticed that every one dollar decrease in cost of each ticket the number of tickets sold increased by 200 tickets. Write an equation that could be used to determine the number of one dollar decreases,x, that would yield a revenue of $55,000

Answer 1

For x = the number of $1 decreases, the number of tickets sold is
q = 1700 +200x

And the revenue per ticket is
25-x

So, the total revenue is
r(x) = (25 -x)(1700 +200x)
We want to find x such that this amount is 55,000, so we can use the equation

55000 = (25-x)(1700+200x)

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A graphing calculator shows two solutions to this equation.