Question
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: Power tools, Cost$: d, 15% discount
Present: Water skis, Cost$: d + 15, 25% discount
Present: Jewelry, Cost$: d - 5, 10% discount
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 $100. Calculate the total cost of each of the possible presents for the value you chose. Then write a short paragraph telling Winona and Takoda which present they should buy and explaining why.
Winona and Takoda are shopping for a present for their mother. The chart shows several possible presents. There is no sales tax in the state where they live.
Present: Power tools, Cost$: d, 15% discount
Present: Water skis, Cost$: d + 15, 25% discount
Present: Jewelry, Cost$: d - 5, 10% discount
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.
Answers
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Answered by
GPT-4o mini
a. To find the total amount Winona and Takoda would pay for the power tools after the discount, we first need to apply the 15% discount to the cost of the power tools. The original cost is \(d\).
The discount amount is:
\[
0.15 \times d = 0.15d
\]
The amount they would pay after the discount is:
\[
d - 0.15d = 0.85d
\]
So, the total amount they would pay for the power tools is:
\[
0.85d
\]
b. The expression \(0.90(d - 5)\) refers to the total amount paid for the jewelry after applying a 10% discount to the original price of the jewelry, which costs \(d - 5\).
To explain:
- The expression \(d - 5\) represents the original cost of the jewelry.
- Since a 10% discount is applied, the customer pays 90% of the original price. Therefore, the calculation becomes \(0.90(d - 5)\).
The expression can also be rewritten as:
\[
0.90(d - 5) = 0.90d - 4.5
\]
c. Let's choose a value for \(d\) in the given range. For example, let's take \(d = 50\).
Now we can calculate the total cost of each present using this value:
1. **Power tools**:
\[
\text{Cost} = 0.85d = 0.85 \times 50 = 42.50
\]
2. **Water skis**:
\[
\text{Cost} = (d + 15) \times (1 - 0.25) = (50 + 15) \times 0.75 = 65 \times 0.75 = 48.75
\]
3. **Jewelry**:
\[
\text{Cost} = 0.90(d - 5) = 0.90 \times (50 - 5) = 0.90 \times 45 = 40.50
\]
### Summary of costs:
- Power tools: $42.50
- Water skis: $48.75
- Jewelry: $40.50
Based on the calculations, Winona and Takoda should consider buying the jewelry, as it has the lowest price at $40.50 after applying the discount. Additionally, the power tools are only slightly more expensive at $42.50, which still makes them a good option if they prefer a more practical gift. However, if they want to stay within a tighter budget, the jewelry offers the best value.
The discount amount is:
\[
0.15 \times d = 0.15d
\]
The amount they would pay after the discount is:
\[
d - 0.15d = 0.85d
\]
So, the total amount they would pay for the power tools is:
\[
0.85d
\]
b. The expression \(0.90(d - 5)\) refers to the total amount paid for the jewelry after applying a 10% discount to the original price of the jewelry, which costs \(d - 5\).
To explain:
- The expression \(d - 5\) represents the original cost of the jewelry.
- Since a 10% discount is applied, the customer pays 90% of the original price. Therefore, the calculation becomes \(0.90(d - 5)\).
The expression can also be rewritten as:
\[
0.90(d - 5) = 0.90d - 4.5
\]
c. Let's choose a value for \(d\) in the given range. For example, let's take \(d = 50\).
Now we can calculate the total cost of each present using this value:
1. **Power tools**:
\[
\text{Cost} = 0.85d = 0.85 \times 50 = 42.50
\]
2. **Water skis**:
\[
\text{Cost} = (d + 15) \times (1 - 0.25) = (50 + 15) \times 0.75 = 65 \times 0.75 = 48.75
\]
3. **Jewelry**:
\[
\text{Cost} = 0.90(d - 5) = 0.90 \times (50 - 5) = 0.90 \times 45 = 40.50
\]
### Summary of costs:
- Power tools: $42.50
- Water skis: $48.75
- Jewelry: $40.50
Based on the calculations, Winona and Takoda should consider buying the jewelry, as it has the lowest price at $40.50 after applying the discount. Additionally, the power tools are only slightly more expensive at $42.50, which still makes them a good option if they prefer a more practical gift. However, if they want to stay within a tighter budget, the jewelry offers the best value.
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