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

So here's the solution to the problem:

Calculate the average sell:

1,700 * $25 = $42,500 (revenue)

And if the Opera House wants to increase their revenue:

The price of a ticket will be:

$25 - x (where x is the number of 1-dollar decreases)

The number of tickets in total:

1,700 + 200x

Therefore the equation is:

(1,700 +200x) * ( 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)