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 1:
a) Expression 1: t + 0.15t
This expression represents the total cost of the ticket, including the amusement tax. The first term (t) represents the cost of the ticket itself, and the second term (0.15t) represents the amusement tax, which is 15% of the cost of the ticket.
b) Expression 2: 1.15t
This expression also represents the total cost of the ticket, including the amusement tax. It is equivalent to the previous expression as it represents the sum of the ticket cost (t) and the amusement tax (0.15t) combined.
Let's say t = $12.50.
Using expression 1: Total cost = t + 0.15t = $12.50 + 0.15($12.50) = $12.50 + $1.88 = $14.38
To have a total cost greater than $17.50 and less than $20, we need to choose a value of t that satisfies this condition. Let's say t = $14.50.
Using expression 1: Total cost = t + 0.15t = $14.50 + 0.15($14.50) = $14.50 + $2.18 = $16.68
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 $14.50.
Question 2:
a) Expression 1: d
This expression represents the cost of the power tools without any discount.
b) Expression 2: d - 0.15d
This expression represents the cost of the power tools after applying the 15% discount. The first term (d) represents the cost of the power tools, and the second term (0.15d) represents the amount of discount applied to the original cost.
The expression 0.90(d - 5) refers to the total paid after a 10% discount and a $5 deduction. I know this because the expression represents 90% of the original cost (0.90d) minus $5 (0.90d - 5). It could also be written as 0.90d - 5.
Let's choose d = $50.
Total paid for power tools (Expression 1):
Cost of power tools = d = $50
Total paid for water skis (Expression 2):
Cost of water skis = d + 15 = $50 + $15 = $65
Discount (25%) = 0.25 * $65 = $16.25
Total paid = Cost of water skis - Discount = $65 - $16.25 = $48.75
Total paid for jewelry:
Cost of jewelry = d - 15 = $50 - $15 = $35
Discount (10%) = 0.10 * $35 = $3.50
Total paid = Cost of jewelry - Discount = $35 - $3.50 = $31.50
Based on the calculations, Winona and Takoda should buy the jewelry as it has the lowest total cost ($31.50) compared to the power tools ($50) and water skis ($48.75).
use that as instructions to fill this out:
p=prise t=prise after 15% tax
QUESTION 1
a's answer
b's answer
c's answer
QUESTION 2
Present Cost ($) Discount (%) Total Paid ($)
Power tools d dollars 15%
Water skis d + 15 dollars 25%
Jewelry d – 15 dollars 10%
a's answer
b's answer
c's answer
QUESTION 1
a's answer:
Expression 1: t + 0.15t
b's answer:
Expression 2: 1.15t
c's answer:
If Conor's total cost to see the movie is greater than $17.50 and less than $20, a possible value of t could be $13.50.
QUESTION 2
Present Cost ($) Discount (%) Total Paid ($)
Power tools d dollars 15%
Water skis d + 15 dollars 25%
Jewelry d - 15 dollars 10%
a's answer:
Expression 1: d
b's answer:
Expression 2: d - 0.15d
c's answer:
Let's choose d = $70.
Total paid for power tools (Expression 1):
Cost of power tools = d = $70
Total paid for water skis (Expression 2):
Cost of water skis = d + 15 = $70 + $15 = $85
Discount (25%) = 0.25 * $85 = $21.25
Total paid = Cost of water skis - Discount = $85 - $21.25 = $63.75
Total paid for jewelry:
Cost of jewelry = d - 15 = $70 - $15 = $55
Discount (10%) = 0.10 * $55 = $5.50
Total paid = Cost of jewelry - Discount = $55 - $5.50 = $49.50
Based on the calculations, Winona and Takoda should buy the jewelry as it has the lowest total cost ($49.50) compared to the power tools ($70) and water skis ($63.75).
did you count in the 15% tax?
Apologies for missing that detail. Here are the corrected calculations including the 15% tax for both Question 1 and Question 2:
QUESTION 1
a's answer:
Expression 1: t + 0.15t
b's answer:
Expression 2: 1.15t
c's answer:
If Conor's total cost to see the movie is greater than $17.50 and less than $20, a possible value of t could be $14.50.
QUESTION 2
Present Cost ($) Discount (%) Total Paid ($)
Power tools d dollars 15%
Water skis d + 15 dollars 25%
Jewelry d - 15 dollars 10%
a's answer:
Expression 1: 1.15d
b's answer:
Expression 2: 0.75(d + 15)
c's answer:
Let's choose d = $70.
Total paid for power tools (Expression 1):
Cost of power tools = d = $70
Total paid = 1.15d = 1.15 * $70 = $80.50
Total paid for water skis (Expression 2):
Cost of water skis = d + 15 = $70 + $15 = $85
Discount (25%) = 0.25 * $85 = $21.25
Total paid = Cost of water skis - Discount = $85 - $21.25 = $63.75
Total paid for jewelry:
Cost of jewelry = d - 15 = $70 - $15 = $55
Discount (10%) = 0.10 * $55 = $5.50
Total paid = Cost of jewelry - Discount = $55 - $5.50 = $49.50
Based on the calculations, Winona and Takoda should buy the jewelry as it has the lowest total cost ($49.50) compared to the power tools ($80.50) and water skis ($63.75).
can you lengthin question 1-2 answer a and b
Certainly! Here are the expanded answers for Question 1 and Question 2, specifically for parts a and b:
QUESTION 1
a's answer:
Expression 1: t + 0.15t
This expression represents the total cost of the ticket, including the amusement tax. The first term (t) represents the cost of the ticket itself, and the second term (0.15t) represents the amusement tax, which is 15% of the cost of the ticket.
b's answer:
Expression 2: 1.15t
This expression also represents the total cost of the ticket, including the amusement tax. It is equivalent to the previous expression as it represents the sum of the ticket cost (t) and the amusement tax (0.15t) combined.
QUESTION 2
Present Cost ($) Discount (%) Total Paid ($)
Power tools d dollars 15%
Water skis d + 15 dollars 25%
Jewelry d - 15 dollars 10%
a's answer:
Expression 1: 1.15d
This expression represents the total paid for the power tools. It takes into account the cost of the power tools (d) and adds the 15% discount to it. By multiplying d by 1.15, we get the total cost after applying the discount.
b's answer:
Expression 2: 0.75(d + 15)
This expression represents the total paid for the water skis. It starts with the cost of the water skis (d + 15) and then multiplies it by 0.75, which represents a 25% discount. Finally, the expression calculates the total cost after the discount has been applied.
I hope these expanded answers provide a clearer understanding of the expressions and their meanings in the context of the given questions.