Have you ever tried to go to the movies, just to find that all the shows were sold out? It’s frustrating for audiences, but it’s also frustrating for theaters! A sold-out show is a sign that they may have been able to charge a higher price for admission. However, higher prices might also mean that fewer people are willing to buy tickets...what is a theater owner to do?

In this lesson, students figure out how much money theaters could make by charging different ticket prices. They find the best possible ticket price, accounting for the fact that theaters would sell fewer tickets at higher prices. Finally, students come up with strategies theaters could use to earn the dollars of audience members willing to pay different amounts.

### Students will

• Calculate the revenue a theater would make from a sold-out show for various ticket prices
• Calculate how much money the theater could be claiming from patrons willing to pay more
• Explain why a sold-out show is not necessarily a good thing, if people willing to pay more did not get in
• Find and graph how many tickets would be sold, and how much revenue collected, for higher ticket prices
• Decide on the best possible ticket price for a given group of moviegoers willing to pay different amounts
• Explain strategies theaters could use to charge different prices to different people, to capture more dollars

### Before you begin

Students should be able to translate a situation into a numerical expression involving multiplication and addition, and plot points in quadrant one.