Problem:

Question

The rock group Loco Moco was scheduled for a concert at the Blaisdell Concert Hall. Because it was the concert highlight of the year, there was excitement in the air and people were eager to get tickets, which could only be purchased in person. Hours before tickets were to go on sale, people were lined up to buy tickets. In fact, the first person came 12 hours before the ticket booth was open. A new group of ticket buyers joined the line every 30 minutes.

Mission:

If each new group has four persons more than the previous group, how many people were in line after the 20th group joined, assuming the first person is the first group?
What did you notice about the number of people who arrived in each successive group?
How many times did four more people arrive?
If each new group had two persons more, how do you think the number in line after the 20th group joined compares to the number of people in line when four people joined as described in problem 1? Explain your reasoning.
What patterns do you see in the numbers of people in each group in problem 2 and the numbers of people in each group in problem 1?
Why do those patterns make sense?
What will the graph look like for the number of people arriving in each group in problem 2?
How will it compare to the graph for problem 1?
How many people were in line 3 hours before the ticket booth opened?
How did your model for solving problems 1 and 2 help you to solve problem 3? Explain your method.