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. The price of a movie ticket is $12.49. Use one of the expressions you wrote in part a to find Conor’s total cost, rounded to the nearest penny. Show your work.

Answer 1

a. To find the total cost of a movie ticket including the amusement tax, we need to calculate the tax as a percentage of the ticket price. The amusement tax is 15% of the ticket price \( t \).

The tax can be expressed as: \[ \text{Tax} = 0.15t \]

The total cost is then the sum of the original ticket price and the tax: \[ \text{Total Cost} = t + 0.15t \] We can also factor this expression as: \[ \text{Total Cost} = 1t + 0.15t = 1.15t \]

Thus, we have two expressions showing Conor's total cost:

1. \( t + 0.15t \)
2. \( 1.15t \)

b. If the price of a movie ticket is \( t = 12.49 \), we can use one of the expressions to find Conor’s total cost. We will use the expression \( 1.15t \):

\[ \text{Total Cost} = 1.15 \times 12.49 \]

Now, we calculate it: \[ 1.15 \times 12.49 = 14.2885 \]

Rounding to the nearest penny, Conor's total cost is: \[ \text{Total Cost} \approx 14.29 \]

Thus, Conor’s total cost, rounded to the nearest penny, is $14.29.

Answer 2

make it shorter only use numbers

Answer 3

a.

1. \( t + 0.15t \)
2. \( 1.15t \)

b.

\( t = 12.49 \)
Total Cost = \( 1.15 \times 12.49 = 14.2885 \)
Rounded: $14.29

Answer 4

c. Suppose that Conor’s total cost to see the movie is greater than $17.50 and
less than $20. What could be a value of t to make that possible?

Answer 5

To find a value of \( t \) such that Conor’s total cost (given by \( 1.15t \)) is greater than $17.50 and less than $20, we can set up the following inequality:

\[ 17.50 < 1.15t < 20 \]

Now, we'll solve the two parts of the inequality:

1. For the left side: \[ 17.50 < 1.15t \] Dividing both sides by \( 1.15 \): \[ t > \frac{17.50}{1.15} \approx 15.2174 \]

2. For the right side: \[ 1.15t < 20 \] Dividing both sides by \( 1.15 \): \[ t < \frac{20}{1.15} \approx 17.3913 \]

Combining these results, we have: \[ 15.22 < t < 17.39 \]

Thus, a possible value for \( t \) could be any value between \( 15.22 \) and \( 17.39 \). For example, \( t = 16.00 \) would work.