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.

Let's go through the given questions step by step.

Part a

1. The cost before tax: \[ \text{Cost before tax} = t \]

2. The amusement tax is 15% of the ticket price: \[ \text{Tax} = 0.15 \times t \]

3. The total cost including the tax: \[ \text{Total cost} = t + 0.15t = 1.15t \]

Therefore, the two expressions for the total cost are:

• \( t \) (cost before tax)
• \( 1.15t \) (total cost with tax)

Part b

Given the ticket price \( t = 11.50 \):

Using the expression for total cost: \[ \text{Total cost} = 1.15t \]

Substituting \( t \): \[ \text{Total cost} = 1.15 \times 11.50 \]

Calculating it: \[ 1.15 \times 11.50 = 13.225 \]

Rounding to the nearest penny: \[ \text{Total cost} \approx 13.23 \]

Conor’s total cost is $13.23.

Part c

To find the value of \( t \) when the total cost is $18.40, we set up the equation using the total cost expression:

\[ 1.15t = 18.40 \]

Now, solve for \( t \): \[ t = \frac{18.40}{1.15} \]

Calculating it: \[ t \approx 16.00 \]

Thus, the value of \( t \) that makes Conor's total cost $18.40 is $16.00.