Question

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.

Answer 1

To calculate the total cost Winona and Takoda would pay for the presents listed, we need to first develop the expressions for the power tools and then evaluate each present using a specific value for \(d\).

Expressions for Total Cost

1. Power Tools:

   • Cost before discount: \( d \)
   • Discount: \( 15% \) of \( d \) = \( 0.15d \)
   • Total Paid after discount: \[ d - 0.15d = 0.85d \]

2. Total Paid for the power tools: \[ 0.85d \]

Expression Analysis

The expression \( 0.90(d - 5) \):

• This expression calculates the total cost after applying a discount. Specifically:
  • First, \( d - 5 \) implies that there's an initial reduction of $5 from the original cost \(d\).
  • Then, \( 0.90 \) indicates a 10% discount is applied to the remaining amount.

This suggests a total amount of \( d - 5 \) before a final 10% discount is taken, resulting in paying 90% of that adjusted cost.

This expression could also be written as: \[ 0.90d - 4.5 \]

Chosen Value for \(d\)

Let’s select \( d = 40 \) (which is greater than $25 and less than $100) and calculate the total cost for each present.

1. Power Tools: \[ 0.85(40) = 34 \]

2. Water Skis:

   • Original cost: \( d + 15 = 40 + 15 = 55 \)
   • Discount: \( 25% \) of \( 55 = 0.25(55) = 13.75 \)
   • Total Paid: \[ 55 - 13.75 = 41.25 \]

3. Jewelry:

   • Original cost: \( d - 15 = 40 - 15 = 25 \)
   • Discount: \( 10% \) of \( 25 = 0.10(25) = 2.5 \)
   • Total Paid: \[ 25 - 2.5 = 22.5 \]

Summary of Total Costs

• Power Tools: $34
• Water Skis: $41.25
• Jewelry: $22.5

Recommendation Paragraph

Based on the total costs calculated, I recommend Winona and Takoda buy the jewelry for their mother, as it totals only $22.5, making it the most affordable option. While the power tools are a worthwhile gift at $34, selecting the jewelry allows them to save more money while still giving a thoughtful present. The water skis, even though fun, are the most expensive at $41.25, which is less cost-effective. Thus, jewelry stands out as a loving and considerate gift that fits comfortably within their budget.

Answer 2

So what are the answers?

Answer 3

Here’s a summary of the answers to the problem:

Expressions for Total Cost

1. Power Tools Total Cost: \[ 0.85d \]

What the Expression \( 0.90(d - 5) \) Refers To

• Meaning: This expression calculates a total payment after deducting $5 from \(d\) and then applying a 10% discount on that reduced amount.
• Alternate Form: It can also be expressed as: \[ 0.90d - 4.5 \]

Chosen Value for \(d\)

• Value Chosen: \( d = 40 \)

Calculated Total Costs for Each Present

1. Power Tools: \[ 34 \text{ dollars} \] (calculated as \(0.85 \times 40\))

2. Water Skis: \[ 41.25 \text{ dollars} \] (calculated as \(55 - 13.75\))

3. Jewelry: \[ 22.5 \text{ dollars} \] (calculated as \(25 - 2.5\))

Recommendations

• Best Option: Jewelry at $22.5 (the most affordable and thoughtful gift).
• Power Tools Total: $34
• Water Skis Total: $41.25

Summary

Winona and Takoda should purchase jewelry for their mother as it's the least expensive option at $22.5 while still being a meaningful gift.