Question

It costs the theater $750 to put on each performance. If tickets are $8 each, how many tickets must they sell at their next performance to profit at least $1200?

Answer 1

The theater needs to sell at least 244 tickets at $8 each to make a profit of at least $1200, since selling 243 tickets would not cover the $1200 profit margin when including the $750 cost for the performance.

Step-by-step explanation:

To calculate how many tickets the theater must sell to make a profit of at least $1200 after costs, we'll set up a simple equation. First, let's denote the number of tickets that need to be sold as x. The total revenue from selling x tickets at $8 each is $8x. We know the theater's costs are $750 per performance, so to make a profit of at least $1200, we want the revenue to exceed costs by $1200. Therefore, our equation is:

$8x - $750 = $1200

Adding $750 to both sides, we get:

$8x = $1200 + $750

$8x = $1950

Dividing both sides by $8 to solve for x, we find:

x = $1950 / $8

x = 243.75

Since you cannot sell a fraction of a ticket, the theater needs to sell at least 244 tickets to meet the goal of a $1200 profit.