Question

Part B

Now we'll change the scenario a bit. The venue needs to project ticket prices for a different upcoming event, and it will
use the information you just found to price the tickets. Here's what we know about the upcoming event:
• The goal is to achieve 100% capacity.
• The average of the maximums you found in the last question is the revenue goal it wants to meet or exceed for this
event. So, the venue wants to make that amount or more.
It also knows that people are less likely to pay as much to attend this event as they paid for tickets to the previous event.
So they want to figure out how much they will have to lower ticket prices to meet their revenue goal and reach 100%
capacity.
Answer the following questions to help the venue meet these goals.
Question 1
The venue's projections indicate that people will buy three times as many of the cheaper tickets than the more expensive
ones. How many tickets of each type should it expect to sell, considering the capacity of the venue?

Answer 1

To achieve 100% capacity with a ratio of three cheaper tickets to one expensive ticket in a venue of 15,000 seats, solve the equation 4x = 15,000, with 'x' representing the number of expensive tickets and '3x' the cheaper tickets.

Step-by-step explanation:

The question revolves around the concept of price elasticity of demand and ticket sales. The venue has a total capacity of 15,000 seats and wishes to achieve 100% capacity while setting a new pricing strategy for an upcoming event. Given the projection that consumers will purchase three cheaper tickets for every one expensive ticket, the venue needs to calculate the proportion of each type of ticket to sell. If 'x' represents the number of expensive tickets, then '3x' will represent the number of cheaper tickets. To achieve full capacity, these must add up to 15,000 seats, leading to the equation x + 3x = 15,000 or 4x = 15,000. Solve for x to find the number of expensive tickets, and multiply by 3 to find the number of cheaper tickets.