Question

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. 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 an average sell:
1,700 * $25 = $42,500 ( revenue )
If the Opera House wants to increase a revenue:
Price of a ticket:  $25 - x ( where x is the number of 1-dollar decreases )
Number of tickets: 1,700 + 200 x
Therefore an equation is:
( 1,700 + 200 x ) * ( 25 - x ) = 55,000
We can also solve this equation, but the solutions are not whole numbers.
x 1 = 5.89 and x 2 = 10.6.
For x = 6 ( 6 times 1-dollar decreases ):
( 1,700 + 200 * 6 ) * ( 25 - 6 ) = ( 1,700 + 1,200 ) * 18 =
= 2,900 * 19 = 55,100 ( we will yield the revenue over $55,000 ).