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.
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 = $0.85d 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.
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 paid for a present, where the original cost of the present is d dollars and there is a discount of 10%.
I know this because the expression includes the term (d - 5), which represents the original cost of the present minus the discount of 5%. The expression is then multiplied by 0.90, which represents a 10% discount as a decimal.
This expression could also be written as 0.90d - 4.5, where the expression (d - 5) is expanded to distribute the 0.90.
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 d = $50 as the value for the present.
1. Power Tools:
Total Paid = 0.85($50) = $42.50
2. Water Skis:
Total Paid = 0.75($50 + 15) = 0.75($65) = $48.75
3. Jewelry:
Total Paid = 0.95($50 - 5) = 0.95($45) = $42.75
Based on the calculations, the total cost for the three presents are as follows:
- Power Tools: $42.50
- Water Skis: $48.75
- Jewelry: $42.75
Considering their budget, it seems that Winona and Takoda should buy the Power Tools for their mother. With a total cost of $42.50, it is within their chosen range for the present. Additionally, it offers the lowest price compared to the Water Skis and Jewelry. Therefore, choosing the Power Tools would be a cost-effective option for them.
Town Census Population Percentage Change
Pleasantville x –2%
Amity Center y +5%
Harmony Corners z +7%
a. Choose one of these towns. Use the second and third columns to write two
expressions showing the current estimated population of the town in terms of
x, y, or z.
Let's choose the town Amity Center, represented by the variable y.
The expressions showing the current estimated population of Amity Center in terms of y would be:
1. Current Estimated Population = y + (0.05y) = 1.05y
2. Current Estimated Population = 1.05y
Both expressions represent the population of Amity Center, taking into account the 5% increase in population, based on the variable y.
Add a fourth row to the table showing the population information for the town
of Concord. Concord’s population as of the last census was p people; for its
percentage change, choose a negative integer not divisible by two. Write two
expressions showing the current estimated population of Concord in terms of p.
Sure! Adding a fourth row to the table:
Town Census Population (%) Percentage Change
Pleasantville x -2%
Amity Center y +5%
Harmony Corners z +7%
Concord p -9%
To show the current estimated population of Concord in terms of p, we can use the percentage change of -9%.
The two expressions showing the current estimated population of Concord in terms of p would be:
1. Current Estimated Population = p + (-0.09p) = 0.91p
2. Current Estimated Population = 0.91p
Both expressions represent the population of Concord, taking into account the 9% decrease in population, based on the variable p.
Choose a number greater than 5,000 and less than 10,000 for the value of p.
Based on the percentage change you chose in part b, calculate the estimated
current population of Concord, rounding to the nearest whole number if
needed. Explain why you used the expression you did to make your calculation.
Let's choose p = 6,500 as the value for the population of Concord.
Using the expression:
Current Estimated Population = 0.91p
Plugging in p = 6,500:
Current Estimated Population = 0.91 * 6,500 = 5,915
Rounding to the nearest whole number, the estimated current population of Concord is 5,915.
I used the expression 0.91p because the percentage change for Concord is a negative 9%. Multiplying p by 0.91 accounts for the 9% decrease in population. By using this expression, we can calculate the estimated current population of Concord based on the last known census population.
A’Leila is building a pen for her pet donkey. The pen is a rectangle with one side
measuring b yards and the adjacent side measuring a yards. A’Leila knows that
a=1/3b
Write two different expressions giving the perimeter of the donkey’s pen.
To find the perimeter of the donkey's pen, we need to add up the lengths of all four sides.
Given that a = 1/3b, we can write two different expressions for the perimeter:
1. Perimeter = a + b + a + b = 2a + 2b
2. Perimeter = (1/3b) + b + (1/3b) + b = (2/3)b + 2b
Both expressions represent the sum of the lengths of all four sides of the donkey's pen, accounting for the given relationship between a and b.