Conor is going to the movie theater. A ticket to a movie costs t dollars, and there is a 15% amusement tax on each ticket.

Question

1. Conor buys a ticket to see a movie. Write two expressions in terms of t showing his total cost.
2. choose a value for t greater than $12 and less than $13. Use one of the expressions you wrote in part 1 to find Conor's total cost, rounded to the nearest penny. Show your work.

Answer 1

1. To find Conor's total cost for a movie ticket, we need to consider both the cost of the ticket and the amusement tax.

The cost of the ticket is \( t \) dollars, and the amusement tax is 15% of that ticket cost. The tax can be expressed as:

\[ \text{Tax} = 0.15t \]

So, the total cost of the ticket including tax can be expressed in two different ways:

Expression 1: Total cost with explicit addition of the tax:

\[ \text{Total Cost} = t + 0.15t = 1.15t \]

Expression 2: Total cost using the original ticket cost multiplied by 1.15 (which includes the tax):

\[ \text{Total Cost} = 1.15t \]

2. Now, let's choose a value for \( t \) greater than $12 and less than $13. Let's take \( t = 12.50 \) for our calculations.

Using the expression \( \text{Total Cost} = 1.15t \):

\[ \text{Total Cost} = 1.15 \times 12.50 \]

Now, we will perform the multiplication:

\[ 1.15 \times 12.50 = 14.375 \]

Now we round \( 14.375 \) to the nearest penny:

\[ \text{Total Cost} \approx 14.38 \]

So, Conor's total cost for the movie ticket, including tax, is $14.38.