Question

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.



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

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**.