Bot GPT 4-o mini Let's tackle your questions one by one.
a. Expressions for Power Tools Cost
To find the total paid for the power tools:
- The cost of the power tools is represented as d.
- 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:
-
Power Tools:
- Total Paid = \(0.85d = 0.85(40) = 34\)
-
Water Skis:
- Cost = \(d + 15 = 40 + 15 = 55\)
- Discount = \(25% \text{ of } 55 = 0.25 \times 55 = 13.75\)
- Total Paid = \(55 - 13.75 = 41.25\)
-
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.
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