Question 1 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. 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. Suppose that Conor’s total cost to see the movie is greater than $17.50 and less than $20. What could be a value of t to make that possible? Question 2 Winona and Takoda are shopping for a present for their mother. The chart shows several possible presents. There is no sales tax in the state where they live. Present Cost ($) Discount (%) Total Paid ($) Power tools d dollars 15% Water skis d + 15 dollars 25% Jewelry d – 15 dollars 10% Write two expressions in terms of d to show how much Winona and Takoda would pay in total if they bought their mother the set of power tools. What does the expression 0.90(d – 5) refer to? How do you know? How else could this expression be written? 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. Question 3 A county planner prepares the following table showing population trends in three local towns. The first column gives the name of the town. The second column gives the population as of the last census. The third column gives the estimated increase or decrease in population since that census, expressed as a percentage of the previous population. Town Population Percentage Change Pleasantville x –2% Amity Center y +5% Harmony Corners z +7% Choose one of these towns. Use the information from the second and third columns to write two expressions showing the current estimated population of the town in terms of x, y, or z. 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. 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) above, 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. Question 4 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=(13)b . Write two different expressions giving the perimeter of the donkey’s pen. Choose a value for a that is greater than 5 and less than 15. Evaluate the perimeter of the pen for that value, using one of the expressions that you wrote. Explain why you used that expression to evaluate the perimeter of the donkey’s pen.

Answer 1

Question 1:

a) The expression for Conor's total cost after the amusement tax would be t + 0.15t, as the tax is 15% of the ticket price.

b) If Conor's total cost is greater than $17.50 and less than $20, we can say that t + 0.15t is greater than $17.50 and less than $20. Let's solve this inequality:

17.50 < t + 0.15t < 20
17.50 < 1.15t < 20
15.22 < t < 17.39

Therefore, a possible value for t could be $16.

Question 2:

a) The expression for the total cost if they bought the set of power tools would be 0.85d, as they have a 15% discount on the original cost.

b) The expression 0.90(d - 5) refers to the total paid after a 10% discount on an item that originally cost d - $5. We know this because it says in the chart that there is a 10% discount on jewelry, which has a cost of d - $15.

This expression could also be written as 0.9d - 4.5.

Let's choose d = $50 and calculate the total cost for each present:

Total cost for power tools = 0.85(50) = $42.50
Total cost for water skis = 0.75(50 + 15) = $48.75
Total cost for jewelry = 0.90(50 - 15) = $31.50

Based on the calculations, Winona and Takoda should buy the set of power tools because it has the lowest total cost of $42.50.

Question 3:

Let's choose the town of Pleasantville.

a) The expression for the current estimated population of Pleasantville in terms of x would be x - 0.02x = 0.98x, as there is a 2% decrease in population.

b) The expression for the current estimated population of Pleasantville in terms of x would be x + 0.05x = 1.05x, as there is a 5% increase in population.

Let's add a fourth row to the table for the town of Concord:

Town Population Percentage Change
Pleasantville x -2%
Amity Center y +5%
Harmony Corners z +7%
Concord p -3%

The expression for the current estimated population of Concord in terms of p would be p - 0.03p = 0.97p, as there is a 3% decrease in population.

Let's choose p = 7000 and calculate the estimated current population of Concord:

Estimated current population of Concord = 0.97(7000) = 6790 (rounded to the nearest whole number)

We used the expression 0.97p because there is a 3% decrease in population, as indicated by the given percentage change.

Question 4:

The expressions for the perimeter of the donkey's pen would be:

Perimeter = 2a + 2b
Perimeter = 2(13b) + 2b = 26b + 2b = 28b

Let's choose a = 8. Evaluate the perimeter of the pen using the expression 28b:

Perimeter = 28(8) = 224 yards

We used the expression 28b because it represents the sum of all sides of the rectangle (2b + 2a) when a is equal to (13)b.