Plz, ! 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.

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

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

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