Question

For the past several years, the high school theater department has performed a musical in their auditorium. Each year since the first, they have raised ticket prices by $0.25, however the department has also noticed a decline in the number of people attending each year. This year, they are analyzing the ticket prices, attendance, and sales to determine the ticket price that maximizes their sales. The table shows their ticket sales with respect to the number of times they have increased the price of a ticket. Ticket Price Increases 1 2 3 4 5 6 Ticket Sales $4,306.25 $4,375.00 $4,406.25 $4,400.00 $4,356.25 $4,275.00 Select the true statement. A. The independent variable is the number of ticket price increases, and the dependent variable is the ticket sales. B. The independent variable is the ticket sales, and the dependent variable is the number of ticket price increases. C. The independent variable is the ticket sales, and the dependent variable is the ticket price. D. The independent variable is the ticket price, and the dependent variable is the ticket sales.

Answer 1

The independent variable (in this case) is the increase in the price for tickets and goes along the x axis. How the sales respond goes along the y axis. That's why it is called the dependent variable. You do something, whatever you are measuring responds. The response depends on what you do.

So the answer is D. But be careful. There is a snake in the grass in A. It is almost right, but the problem says that they are tracking the ticket sales (in dollars) with respect to increases in the price of each ticket.

There might be fewer people, but they are willing to pay more.

A is not quite correct given the criteria of the problem. The criteria is the selling price of the ticket after the price increases.