You and your friend Alex are looking to buy tickets for a big concert. You know that Ticket System charges $22 per person plus a $10 surcharge per transaction. You and Alex think you can get a better deal at Max Tickets or Ticket Meister, both of which are also selling tickets for the event. Pick one of these two sellers, and use your knowledge of linear systems to compare it with Ticket System and figure out who has the better deal.

1. Which company did you select? (1 point)

Comparing the Prices
2. First, write an equation that represents the cost of tickets from Ticket System. (1 point)

3. Next, write an equation that represents the cost of tickets from the company you chose. (2 points)

4. Some friends have heard about the concert, and now you might have to buy up to five tickets. Use your equations to create a price table for each company. (4 points: 2 points for each company)

5. Now graph the ticket prices for each company on the same pair of axes to compare the values.
(4 points: 2 points for each line)

Analyzing Your Data
Use the price table and your graph to answer the following questions.

6. Why is it helpful to have both lines on the same graph? (2 points)

7. How many people have to buy tickets for the two companies to have the same price? How did you find your answer? (2 points: 1 point for a correct solution, 1 point for an appropriate explanation)

8. When does Ticket System give you a better price? (2 points)

A New Offer
9. Another friend already bought tickets, but now she can't go. She offers to sell you 4 tickets for $100. Is this a better deal than either of the deals you have already analyzed? Explain how you know. (2 points: 1 point for a correct response, 1 point for appropriate explanation)