Conor is going to the movie theater. A ticket to a movie theater 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.

Expression 1: The cost of the ticket without the amusement tax is t.

Expression 2: The total cost with the amusement tax is t + 0.15t = 1.15t.

Choose a value for t greater than $12 in less than $13 use one of the expressions you wrote in part a to find Conors total cost, rounded to the nearest penny show your work

Let's use t = $12.50 for this example.

Using Expression 2:
Total cost = 1.15t
Total cost = 1.15 * $12.50
Total cost = $14.38

Conor's total cost, rounded to the nearest penny, is $14.38.

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?

To find a value of t that makes Conor's total cost greater than $17.50 and less than $20, we can use Expression 2 and solve the inequality:

17.50 < 1.15t < 20

Divide both sides of the inequality by 1.15:

15.22 < t < 17.39

Therefore, a possible value for t could be between approximately $15.22 and $17.39.

Complete the following questions.

Winona and Takoda are shopping for a present for their mother. The chart shows several possible presents. There is no sales tax in the state where they live.
Present
Power tools Water skis Jewelry
Cost ($) Discount (%) Total Paid
d 15% d + 15 25% d – 5 10%
a. Write two expressions in terms of d to show how much Winona and Takoda would pay in total if they buy their mother the set of power tools.

Expression 1: Total cost after the 15% discount: (100% - 15%)d = 0.85d.

Expression 2: Total cost after the 10% jewelry discount: (100% - 10%)d = 0.90d.

What does the expression 0.90(d – 5) refer to? How do you know? How else could this expression be written?

The expression 0.90(d - 5) refers to the total cost Winona and Takoda would pay if they buy their mother the jewelry present.

I know this because the expression involves a discount of 10% off the original price (d - 5) and then the total cost is found by multiplying this discounted price by 0.90 (to account for the remaining 90% of the original price).

The expression 0.90(d - 5) could also be written as 0.90d - 4.50.

Choose a value for d that is greater than $25 and less than $100. Calculate the total cost of each of the possible presents for the value you chose. Then write a short paragraph telling Winona and Takoda which present they should buy and explaining why.

Let's choose a value for d = $50 for this example.

For the power tools:
Total cost = 0.85d
Total cost = 0.85 * $50
Total cost = $42.50

For the water skis:
Total cost = (100% - 15%)d + 15
Total cost = 0.85d + 15
Total cost = 0.85 * $50 + $15
Total cost = $42.50 + $15
Total cost = $57.50

For the jewelry:
Total cost = (100% - 10%)d – 5
Total cost = 0.90d - 5
Total cost = 0.90 * $50 - $5
Total cost = $45 - $5
Total cost = $40

Based on these calculations, Winona and Takoda should buy the power tools. The total cost for the power tools is $42.50, which is lower than the total cost of the water skis $57.50 and the jewelry $40. Therefore, the power tools would be the best choice as it offers the lowest cost option among the three presents for their chosen value of d ($50).