Question
Question 1:
Connor is going to the movie theater. A ticket to a movie costs t dolllars, and there is a 15% amusement tax on each ticket.
A. Connor buys a ticket to see a movie. Write 2 expressions in term of t showing his total cost.+2
B. Choose a value for t is $11.50. Use one of the expressions u wrote n part a to find Connors total cost, rounded to the nearest penny. Show work +2
C. Suppose Connors total cost to see the movie is $ 18.40 what is the value of t to make that possible? +2
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
Power tools
Water
Jewelry
COST ( $ )
d
d + 15
d - 5
DISCOUNT ( % )
15%
25%
10%
TOTAL PAID
( +2 )
( +2 )
( +2 )
A. Write two expressions in term of d to show how much Winona and Takoda would pay in total if they but their mother the set of power tools.
B. What present does the expression 0.90 ( d -5 ) refer to?
C. Use the value d=$50. Calculate the TOTAL PAID ( +6pts see above ) Column of each of the possible presents for the value of $50. Then star or circle the most economical or cheapest ( +1 )
Connor is going to the movie theater. A ticket to a movie costs t dolllars, and there is a 15% amusement tax on each ticket.
A. Connor buys a ticket to see a movie. Write 2 expressions in term of t showing his total cost.+2
B. Choose a value for t is $11.50. Use one of the expressions u wrote n part a to find Connors total cost, rounded to the nearest penny. Show work +2
C. Suppose Connors total cost to see the movie is $ 18.40 what is the value of t to make that possible? +2
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
Power tools
Water
Jewelry
COST ( $ )
d
d + 15
d - 5
DISCOUNT ( % )
15%
25%
10%
TOTAL PAID
( +2 )
( +2 )
( +2 )
A. Write two expressions in term of d to show how much Winona and Takoda would pay in total if they but their mother the set of power tools.
B. What present does the expression 0.90 ( d -5 ) refer to?
C. Use the value d=$50. Calculate the TOTAL PAID ( +6pts see above ) Column of each of the possible presents for the value of $50. Then star or circle the most economical or cheapest ( +1 )
Answers
GPT-4o mini
### Question 1
#### A.
To determine Connor's total cost when he buys a ticket to see a movie, we have to account for the ticket price and the amusement tax.
1. **Cost of the ticket alone**: \( t \)
2. **Amusement tax (15% of ticket price)**: \( 0.15t \)
Therefore, the total cost (TC) will be the sum of the ticket price and the tax:
\[
\text{Total Cost} = t + 0.15t
\]
This can also be expressed as:
\[
\text{Total Cost} = 1.15t
\]
#### B.
Choosing a value for \( t \) as $11.50, we can calculate Connor's total cost using the expression we derived:
\[
\text{Total Cost} = 1.15 \times 11.50
\]
Calculating this:
\[
\text{Total Cost} = 13.225
\]
Rounding to the nearest penny, Connor's total cost is:
\[
\text{Total Cost} \approx 13.23
\]
#### C.
If Connor's total cost to see the movie is $18.40, we can use our total cost expression to find the value of \( t \):
\[
1.15t = 18.40
\]
Now, isolate \( t \):
\[
t = \frac{18.40}{1.15}
\]
Calculating this gives:
\[
t = 16.00
\]
So, the value of \( t \) to make that total cost possible is $16.00.
---
### Question 2
#### A.
For the power tools, we need to find two expressions in terms of \( d \):
1. The cost of the power tools before the discount is \( d \).
2. The discount is 15% of \( d \), calculated as \( 0.15d \).
The total paid after the discount can be expressed as:
\[
\text{Total Paid} = d - 0.15d = 0.85d
\]
Thus, an expression in terms of \( d \) for the total paid for power tools is:
\[
\text{Total Paid} = 0.85d
\]
#### B.
The expression \( 0.90(d - 5) \) refers to the jewelry, since the cost of the jewelry before discount is \( d - 5 \) and the discount is 10%.
#### C.
Given \( d = 50 \), we will calculate the total paid for each present:
1. **Power Tools**:
\[
\text{Total Paid} = 0.85 \times 50 = 42.50
\]
2. **Water**:
The cost is \( d + 15 \):
\[
\text{Cost} = 50 + 15 = 65
\]
Now applying the 25% discount:
\[
\text{Total Paid} = 0.75 \times 65 = 48.75
\]
3. **Jewelry**:
The cost is \( d - 5 \):
\[
\text{Cost} = 50 - 5 = 45
\]
Now applying the 10% discount:
\[
\text{Total Paid} = 0.90 \times 45 = 40.50
\]
Now we summarize the total paid for each present:
- Power Tools: $42.50
- Water: $48.75
- Jewelry: $40.50
To identify the most economical or cheapest option, we clearly see that the **Jewelry** at **$40.50** is the cheapest present.
**Final note**: Circle or star the Jewelry in the results list as the most economical option.
#### A.
To determine Connor's total cost when he buys a ticket to see a movie, we have to account for the ticket price and the amusement tax.
1. **Cost of the ticket alone**: \( t \)
2. **Amusement tax (15% of ticket price)**: \( 0.15t \)
Therefore, the total cost (TC) will be the sum of the ticket price and the tax:
\[
\text{Total Cost} = t + 0.15t
\]
This can also be expressed as:
\[
\text{Total Cost} = 1.15t
\]
#### B.
Choosing a value for \( t \) as $11.50, we can calculate Connor's total cost using the expression we derived:
\[
\text{Total Cost} = 1.15 \times 11.50
\]
Calculating this:
\[
\text{Total Cost} = 13.225
\]
Rounding to the nearest penny, Connor's total cost is:
\[
\text{Total Cost} \approx 13.23
\]
#### C.
If Connor's total cost to see the movie is $18.40, we can use our total cost expression to find the value of \( t \):
\[
1.15t = 18.40
\]
Now, isolate \( t \):
\[
t = \frac{18.40}{1.15}
\]
Calculating this gives:
\[
t = 16.00
\]
So, the value of \( t \) to make that total cost possible is $16.00.
---
### Question 2
#### A.
For the power tools, we need to find two expressions in terms of \( d \):
1. The cost of the power tools before the discount is \( d \).
2. The discount is 15% of \( d \), calculated as \( 0.15d \).
The total paid after the discount can be expressed as:
\[
\text{Total Paid} = d - 0.15d = 0.85d
\]
Thus, an expression in terms of \( d \) for the total paid for power tools is:
\[
\text{Total Paid} = 0.85d
\]
#### B.
The expression \( 0.90(d - 5) \) refers to the jewelry, since the cost of the jewelry before discount is \( d - 5 \) and the discount is 10%.
#### C.
Given \( d = 50 \), we will calculate the total paid for each present:
1. **Power Tools**:
\[
\text{Total Paid} = 0.85 \times 50 = 42.50
\]
2. **Water**:
The cost is \( d + 15 \):
\[
\text{Cost} = 50 + 15 = 65
\]
Now applying the 25% discount:
\[
\text{Total Paid} = 0.75 \times 65 = 48.75
\]
3. **Jewelry**:
The cost is \( d - 5 \):
\[
\text{Cost} = 50 - 5 = 45
\]
Now applying the 10% discount:
\[
\text{Total Paid} = 0.90 \times 45 = 40.50
\]
Now we summarize the total paid for each present:
- Power Tools: $42.50
- Water: $48.75
- Jewelry: $40.50
To identify the most economical or cheapest option, we clearly see that the **Jewelry** at **$40.50** is the cheapest present.
**Final note**: Circle or star the Jewelry in the results list as the most economical option.