a. The two expressions in terms of t showing Conor's total cost are:
1) Total cost = t + 0.15t = t(1 + 0.15) = 1.15t (includes the price of the ticket plus the 15% amusement tax)
2) Total cost = t + (0.15)(t) = t + 0.15t = 1.15t (includes the price of the ticket plus the 15% amusement tax)
b. Let's choose t = $12.50. Using the expression 1.15t, Conor's total cost would be:
Total cost = 1.15(12.50) = $14.375
Rounded to the nearest penny, Conor's total cost would be $14.38.
c. To find a value of t that makes the total cost greater than $17.50 and less than $20, we can set up the inequality:
17.50 < 1.15t < 20
Divide all parts of the inequality by 1.15 to isolate t:
15.22 < t < 17.39
Therefore, a possible value of t could be any number between $15.22 and $17.39.
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.
c. Suppose that Conor’s total cost to see the movie is greater than $17.50 and
less than $20. What could be a value of t to make that possible?
7 answers
Question 2
Complete the following questions.
Winona and Takoda are shopping for a present for their mother. The chart shows
several possible presents. There is no sales tax in the state where they live.
Present Cost ($) 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.
b. What does the expression 0.90(d – 5) refer to? How do you know? How else
could this expression be written?
c. Choose a value for d that is greater than $25 and less than $100. Calculate the
total cost of each of the possible presents for the value you chose. Then write a
short paragraph telling Winona and Takoda which present they should buy and
explaining why.
Complete the following questions.
Winona and Takoda are shopping for a present for their mother. The chart shows
several possible presents. There is no sales tax in the state where they live.
Present Cost ($) 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.
b. What does the expression 0.90(d – 5) refer to? How do you know? How else
could this expression be written?
c. 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.
a. Two expressions to show how much Winona and Takoda would pay in total for the set of power tools:
1) Total cost = d - 0.15d = d(1 - 0.15) = 0.85d (includes the cost of the power tools minus the 15% discount)
2) Total cost = d - (0.15)(d) = d - 0.15d = 0.85d (includes the cost of the power tools minus the 15% discount)
b. The expression 0.90(d - 5) refers to the total amount paid if Winona and Takoda buy jewelry. The expression can be written as 0.90d - 0.90(5) = 0.90d - 4.50, which shows the cost of the jewelry (90% of d) with a 10% discount subtracted (0.90 * 5).
c. Let's choose d = $50.
For the power tools, the total cost would be:
Total cost = 0.85(50) = $42.50
For the water skis, the total cost would be:
Total cost = (50 + 15) - 0.25(50+15) = $61.25
For the jewelry, the total cost would be:
Total cost = 0.90(50 - 5) = $40.50
Based on the prices, Winona and Takoda should buy their mother the jewelry. It has the lowest total cost of $40.50.
1) Total cost = d - 0.15d = d(1 - 0.15) = 0.85d (includes the cost of the power tools minus the 15% discount)
2) Total cost = d - (0.15)(d) = d - 0.15d = 0.85d (includes the cost of the power tools minus the 15% discount)
b. The expression 0.90(d - 5) refers to the total amount paid if Winona and Takoda buy jewelry. The expression can be written as 0.90d - 0.90(5) = 0.90d - 4.50, which shows the cost of the jewelry (90% of d) with a 10% discount subtracted (0.90 * 5).
c. Let's choose d = $50.
For the power tools, the total cost would be:
Total cost = 0.85(50) = $42.50
For the water skis, the total cost would be:
Total cost = (50 + 15) - 0.25(50+15) = $61.25
For the jewelry, the total cost would be:
Total cost = 0.90(50 - 5) = $40.50
Based on the prices, Winona and Takoda should buy their mother the jewelry. It has the lowest total cost of $40.50.
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 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.
b. 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.
c. 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
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 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.
b. 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.
c. 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
a. Let's choose the town of Amity Center. The current estimated population of Amity Center can be expressed as:
1) Current population = y + 0.05y = y(1 + 0.05) = 1.05y (population plus 5% increase)
2) Current population = y + (0.05)(y) = y + 0.05y = 1.05y (population plus 5% increase)
b. Adding a row for the town of Concord:
Town | Census Population | Percentage Change
Concord | p | -3%
The expressions showing the current estimated population of Concord would be:
1) Current population = p - 0.03p = p(1 - 0.03) = 0.97p (population minus 3% decrease)
2) Current population = p - (0.03)(p) = p - 0.03p = 0.97p (population minus 3% decrease)
c. Let's choose p = 7,500 as the value for Concord's population.
Using the expression 0.97p, the estimated current population of Concord would be:
Current population = 0.97(7,500) = 7,275
I used the expression 0.97p because the percentage change mentioned in part b was -3%, indicating a decrease in population. By multiplying the previous population (p) by 0.97, we account for the 3% decrease to calculate the estimated current population.
1) Current population = y + 0.05y = y(1 + 0.05) = 1.05y (population plus 5% increase)
2) Current population = y + (0.05)(y) = y + 0.05y = 1.05y (population plus 5% increase)
b. Adding a row for the town of Concord:
Town | Census Population | Percentage Change
Concord | p | -3%
The expressions showing the current estimated population of Concord would be:
1) Current population = p - 0.03p = p(1 - 0.03) = 0.97p (population minus 3% decrease)
2) Current population = p - (0.03)(p) = p - 0.03p = 0.97p (population minus 3% decrease)
c. Let's choose p = 7,500 as the value for Concord's population.
Using the expression 0.97p, the estimated current population of Concord would be:
Current population = 0.97(7,500) = 7,275
I used the expression 0.97p because the percentage change mentioned in part b was -3%, indicating a decrease in population. By multiplying the previous population (p) by 0.97, we account for the 3% decrease to calculate the estimated current 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=1/3 b
.
a. Write two different expressions giving the perimeter of the donkey’s pen.
b. 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.
c. Explain why you used that expression to evaluate the perimeter of the
donkey’s pen
measuring b yards and the adjacent side measuring a yards. A’Leila knows that a=1/3 b
.
a. Write two different expressions giving the perimeter of the donkey’s pen.
b. 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.
c. Explain why you used that expression to evaluate the perimeter of the
donkey’s pen
a. Two different expressions giving the perimeter of the donkey's pen are:
1) Perimeter = 2a + 2b
2) Perimeter = 2(a + b)
b. Let's choose a = 7 yards. Using the expression Perimeter = 2(a + b), the perimeter of the pen would be:
Perimeter = 2(7 + b)
Since we don't have a specific value for b given in the question, we cannot calculate the exact perimeter. However, we can calculate the perimeter relative to a by substituting the given value of a and solving for the perimeter.
Perimeter = 2(7 + b)
Perimeter = 14 + 2b
c. I used the expression Perimeter = 2(a + b) to evaluate the perimeter of the donkey's pen because it allows us to calculate the total distance around the pen by considering the lengths of both sides. By adding a and b together, we account for the length of both adjacent sides of the rectangle, and multiplying the sum by 2 gives us the total distance around the pen.
1) Perimeter = 2a + 2b
2) Perimeter = 2(a + b)
b. Let's choose a = 7 yards. Using the expression Perimeter = 2(a + b), the perimeter of the pen would be:
Perimeter = 2(7 + b)
Since we don't have a specific value for b given in the question, we cannot calculate the exact perimeter. However, we can calculate the perimeter relative to a by substituting the given value of a and solving for the perimeter.
Perimeter = 2(7 + b)
Perimeter = 14 + 2b
c. I used the expression Perimeter = 2(a + b) to evaluate the perimeter of the donkey's pen because it allows us to calculate the total distance around the pen by considering the lengths of both sides. By adding a and b together, we account for the length of both adjacent sides of the rectangle, and multiplying the sum by 2 gives us the total distance around the pen.
55 answers