Vinh pays a convenience fee when he reserves movie ticket son his cell phone app. The app shows him the total cost of his purchase for different number of tickets in the table shown.

Question

What is the equation that models this linear function? Show your work. Don’t forget to define your variables!

Use the phrase is a function of to describe the situation Tickets 2 3 6 Total Cost $32.00 $44.50 $82.00 represented by the equation you wrote in problem 3a.

How much is each movie ticket?

Answer 1

Let's define the variables:
Let x be the number of tickets.
Let y be the total cost.

We can see that the cost of the tickets increases by $12.50 each time the number of tickets increases by 1.

From the table, we can determine that the additional cost for each additional ticket is $12.50.

Therefore, the equation that models this linear function is:
y = 12.50x + b

To find b, we can use the given data point (2, $32.00) in the table:
32 = 12.50(2) + b
32 = 25 + b
b = 32 - 25
b = 7

So the equation becomes:
y = 12.50x + 7

Now, we can describe the situation using the phrase "is a function of":
The total cost (y) is a function of the number of tickets (x).

To find how much each movie ticket costs, we can rearrange the equation:
y = 12.50x + 7
Substituting the given total cost for 1 ticket (x = 1) into the equation:
32 = 12.50(1) + 7
32 = 12.50 + 7
32 - 7 = 12.50
25 = 12.50

Therefore, each movie ticket costs $12.50.