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.

To find the value of \( t \), the cost of a movie ticket before tax, we can set up an equation based on the information provided.

The total cost that Conor pays for the movie ticket includes the ticket price \( t \) and a 15% amusement tax on the ticket. The amount of tax can be expressed as \( 0.15t \).

So the total cost can be calculated as follows:

\[ \text{Total Cost} = t + \text{Tax} \] \[ \text{Total Cost} = t + 0.15t \] \[ \text{Total Cost} = 1t + 0.15t = 1.15t \]

We know that Conor's total cost to see the movie is $18.40. Therefore, we can set up the equation:

\[ 1.15t = 18.40 \]

To find \( t \), we divide both sides of the equation by 1.15:

\[ t = \frac{18.40}{1.15} \]

Now, calculating the right-hand side:

\[ t \approx 16.00 \]

So, the value of \( t \), the original price of the movie ticket, is approximately \( \boxed{16.00} \) dollars.

To calculate the tax on the movie ticket, we first need to confirm the ticket price \( t \). We previously found that \( t \) is approximately $16.00.

The amusement tax is 15% of the ticket price. We can calculate the tax as follows:

\[ \text{Tax} = 0.15 \times t = 0.15 \times 16.00 \]

Now calculating this:

\[ \text{Tax} = 0.15 \times 16.00 = 2.40 \]

Thus, the amount of tax Conor paid was \( \boxed{2.40} \) dollars.