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The Opera House sells an average of 1,700 tickets per night when the price of each ticket is $25. An employee of the Opera House noticed that with every one-dollar decrease in the cost of each ticket, the number of tickets sold increased by 200 tickets.

plz help me 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 with ever class=

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Revenue: R=$55,000

R=pq

Price: p
Quantity: q

when p=$25→q=1,700

With every one-dollar decrease in the cost of each ticket, the number of tickets sold increase by 200 tickets:
p=$25-$1(1)→q=1,700+200(1)
p=$25-$1(2)→q=1,700+200(2)
p=$25-$1(3)→q=1,700+200(3)

Number of one-dollar decreases: x
p=$25-$1(x)→p=25-1x
q=1,700+200(x)→q=1,700+200x

R=pq→( 25 - 1 x )( 1,700 + 200 x ) = 55,000

Answer: ( 25 - 1 x )( 1,700 + 200 x ) = 55,000
Blitztiger
The revenue is the product of the price of the ticket and the number of tickets per night. Beginning from the baseline of $25 * 1700 tickets, we have the relationship that every decrease in price of $1 = (25 - 1x), results in a increase in ticket sales of 200 = (1700 + 200x). This must result in a product of 55,000, so:
(25 - 1x)(1700 + 200x) = 55000