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.
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 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. Show your work.
a. The first expression showing Conor's total cost would be t + (0.15t), which represents the cost of the ticket plus the 15% amusement tax on the ticket.
The second expression showing Conor's total cost would be 1.15t, which represents the cost of the ticket plus the 15% amusement tax as a decimal.
b. Let's choose t = $12.50. Using the first expression, Conor's total cost would be 12.50 + (0.15 * 12.50) = 12.50 + 1.875 = $14.375. Rounded to the nearest penny, Conor's total cost would be $14.38.
a. To calculate Conor's total cost, we need to consider the cost of the movie ticket and the amusement tax.
The expression for the cost of the movie ticket is simply "t dollars".
The expression for the amusement tax is calculated by taking 15% of the ticket price, which can be written as 0.15t dollars.
Therefore, the two expressions in terms of t showing Conor's total cost are:
1. Total cost = t + 0.15t dollars
2. Total cost = 1.15t dollars
b. Let's choose a value for t such as t = $12.50.
Using the first expression, the total cost would be:
Total cost = 12.50 + 0.15(12.50) = 12.50 + 1.875 = $14.375
Rounded to the nearest penny, Conor's total cost would be $14.38.
Note that you can use the same approach with the second expression to calculate the total cost.
a. The two expressions in terms of t showing Conor's total cost are:
1. Total cost without tax: t
2. Total cost with tax: t + 0.15t
b. Let's choose t = $12.50. Using the second expression, we can find Conor's total cost:
Total cost with tax = t + 0.15t = 12.50 + 0.15(12.50) = 12.50 + 1.875 = $14.375
Rounded to the nearest penny, Conor's total cost 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 would make Conor's total cost to see the movie greater than $17.50 and less than $20, we can use the second expression for Conor's total cost with tax:
Total cost with tax = t + 0.15t
We want this total cost to be greater than $17.50 and less than $20. So we can set up the following inequality:
17.50 < t + 0.15t < 20
To solve this inequality, we simplify it by combining like terms:
17.50 < 1.15t < 20
Then we divide each term by 1.15 to isolate t:
17.50/1.15 < t < 20/1.15
This simplifies to:
15.22 < t < 17.39
Therefore, a possible value of t that would make Conor's total cost to see the movie greater than $17.50 and less than $20 is any value between $15.22 and $17.39.
Complete the following questions.
Winona and Takoda are shopping for a present for their mother. The chart shows
several possible presents. There is no sales tax in the state where they live.
Present Cost ($) Discount (%) Total Paid
Power tools d 15%
Water skis d + 15 25%
Jewelry d – 5 10%
To help Winona and Takoda with their shopping decision, let's go through the given information.
1. Power Tools:
Cost: d dollars
Discount: 15%
Total Paid: d - 0.15d = 0.85d dollars
2. Water Skis:
Cost: d + 15 dollars
Discount: 25%
Total Paid: (d + 15) - 0.25(d + 15) = 0.75(d + 15) dollars
3. Jewelry:
Cost: d dollars
Discount: -5% (a negative discount means an increase in price)
Total Paid: d + (d * -0.05) = d - 0.05d = 0.95d dollars
So the expressions for the total paid for each present are as follows:
1. Power Tools: 0.85d dollars
2. Water Skis: 0.75(d + 15) dollars
3. Jewelry: 0.95d dollars
Next, solve the following questions:
a. If the cost of the power tools is $100, what would be the total paid for the power tools?
To find the total paid, substitute d = 100 into the expression for power tools:
Total Paid = 0.85(100) = $85
b. If the cost of the water skis is $200, what would be the total paid for the water skis?
To find the total paid, substitute d = 200 into the expression for water skis:
Total Paid = 0.75(200 + 15) = 0.75(215) = $161.25
c. If the cost of the jewelry is $50, what would be the total paid for the jewelry?
To find the total paid, substitute d = 50 into the expression for jewelry:
Total Paid = 0.95(50) = $47.50
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.
To show how much Winona and Takoda would pay in total if they buy their mother the set of power tools, we can use the expression for the total paid for power tools, which is 0.85d dollars.
The two expressions in terms of d to show how much they would pay in total are:
1. Total Paid = 0.85d dollars
2. Total Paid = $0.85(d) dollars
Both expressions represent the amount they would pay for the set of power tools based on the cost of the tools, represented by d.
Complete the following questions.
Winona and Takoda are shopping for a present for their mother. The chart shows
several possible presents. There is no sales tax in the state where they live.
Present Cost ($) Discount (%) Total Paid
Power tools d 15%
Water skis d + 15 25%
Jewelry 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.