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 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.

Answer 1

Let's tackle your questions one by one.

### a. Expressions for Power Tools Cost

To find the total paid for the power tools:

1. The cost of the power tools is represented as **d**.
2. The discount on power tools is **15%** of **d**.

The amount of discount can be calculated as:
\[
\text{Discount on Power Tools} = 0.15d
\]

Thus, the total amount paid after the discount is applied can be expressed as:
\[
\text{Total Paid} = d - 0.15d = 0.85d
\]

So, Winona and Takoda would pay **0.85d** in total if they buy the power tools.

### b. Expression \(0.90(d - 5)\)

The expression \(0.90(d - 5)\) refers to the total cost Winona and Takoda would pay if they buy the jewelry.

- To break it down:
- \(d - 5\) represents the price of the jewelry after a $5 discount on **d**.
- The 10% discount means they pay 90% of the price after that discount: \(1 - 0.10 = 0.90\).

So the total paid for the jewelry can also be expressed as:
\[
0.90(d - 5)
\]

This expression can also be written in distribution as:
\[
0.90d - 4.5
\]

### c. Choosing a value for d and calculating total costs

Let's choose \(d = 40\) (which is greater than $25 and less than $100).

Now let’s calculate the total costs for each present:

1. **Power Tools:**
- Total Paid = \(0.85d = 0.85(40) = 34\)

2. **Water Skis:**
- Cost = \(d + 15 = 40 + 15 = 55\)
- Discount = \(25\% \text{ of } 55 = 0.25 \times 55 = 13.75\)
- Total Paid = \(55 - 13.75 = 41.25\)

3. **Jewelry:**
- Cost = \(d - 5 = 40 - 5 = 35\)
- Discount = \(10\% \text{ of } 35 = 0.10 \times 35 = 3.5\)
- Total Paid = \(35 - 3.5 = 31.5\)

### Summary Paragraph

After calculating the total costs for the possible presents for their mother with **d = 40**, the total costs are as follows:
- Power tools: $34
- Water skis: $41.25
- Jewelry: $31.50

I would recommend Winona and Takoda buy the jewelry. Even though the power tools are slightly more expensive at $34, the jewelry only costs $31.50 after discounts, making it the most affordable option. Additionally, jewelry is often seen as a thoughtful and sentimental present, which is perfect for their mother.