Question

Question 1
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.
Conor buys a ticket to see a movie. Write two expressions in terms of t
showing his total cost.

Answer 1

Choose a value for t greater than $12 and less than $13. Use one of the
expressions you wrote in part a to find Conor’s total cost, rounded to the
nearest penny. keep your answer short

Answer 2

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? keep answer short

Answer 3

To determine Conor's total cost for the movie ticket, we need to consider both the cost of the ticket and the amusement tax.

1. **Cost of the ticket:** This is simply \( t \) dollars.

2. **Amusement tax:** The amusement tax is 15% of the ticket price. This can be expressed as:
\[
0.15t
\]

3. **Total cost:** The total cost for Conor will therefore be the cost of the ticket plus the amusement tax. This can be expressed as:
\[
t + 0.15t
\]

This simplifies to:
\[
t(1 + 0.15) = t \cdot 1.15 = 1.15t
\]

So, the two expressions showing Conor's total cost in terms of \( t \) are:
1. \( t + 0.15t \)
2. \( 1.15t \)

Both expressions represent the same total cost.

Answer 4

Let's choose \( t = 12.50 \).

Using the expression \( 1.15t \) to find Conor’s total cost:

\[
\text{Total Cost} = 1.15 \times 12.50 = 14.375
\]

Rounding to the nearest penny, Conor's total cost is:

\[
\text{Total Cost} \approx 14.38
\]

Answer 5

To find a value of \( t \) such that \( 17.50 < 1.15t < 20 \), we can manipulate the inequalities:

1. **For the lower bound:**
\[
1.15t > 17.50 \implies t > \frac{17.50}{1.15} \approx 15.22
\]

2. **For the upper bound:**
\[
1.15t < 20 \implies t < \frac{20}{1.15} \approx 17.39
\]

Thus, \( t \) should be in the range:
\[
15.22 < t < 17.39
\]

A possible value of \( t \) in this range could be \( t = 16 \).