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

a. Conor buys a ticket to see a movie. Write TWO expressions in terms of "t" showing his total cost.
b. Choose a value for "t" which is $11.50. Use one of the expressions you wrote in part a to find Conor’s total cost, rounded to the nearest penny. Show your work.
c. Suppose that Conor’s total cost to see the movie is $18.40 What is the value of "t" to make that possible?

Answer 1

a. To express Conor's total cost for the movie ticket including the amusement tax, we can write two expressions in terms of "t":

1. The cost of the ticket without tax: \( t \)
2. The cost of the ticket with the 15% amusement tax: \[ \text{Total cost} = t + 0.15t = 1.15t \]

So, the two expressions showing Conor's total cost are:

1. \( t \)
2. \( 1.15t \)

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b. If we choose \( t = 11.50 \), we can use the total cost expression \( 1.15t \) to find Conor's total cost.

Calculating: \[ 1.15t = 1.15 \times 11.50 \]

Now performing the multiplication: \[ 1.15 \times 11.50 = 13.225 \]

Rounding to the nearest penny: Conor's total cost is \( 13.23 \) dollars.

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c. To find the value of \( t \) that results in a total cost of $18.40, we can set up the equation using the total cost expression:

\[ 1.15t = 18.40 \]

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

Calculating: \[ t = 16.00 \]

So, the value of \( t \) that makes Conor’s total cost $18.40 is \( 16.00 \) dollars.