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 $100. Calculate the total cost of each of the possible presents for the value you chose. Then write a short paragraph telling Winona and Takoda which present they should buy and explaining why.
Winona and Takoda are shopping for a present for their mother. The chart shows several possible presents. There is no sales tax in the state where they live. Present Cost ($) 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.
To calculate the total amount Winona and Takoda would pay if they bought their mother the set of power tools, two expressions in terms of d can be used:
1) Total Paid with a 15% discount:
Total Paid = d - 0.15d = 0.85d
2) Total Paid without a discount:
Total Paid = d
The expression 0.90(d - 5) refers to the total paid when there is a 10% discount subtracted from the original cost (d), and a further $5 reduction. The expression can also be written as 0.90d - 4.5.
Let's choose d = $50 as a value that is greater than $25 and less than $100.
For power tools:
Total Paid with a 15% discount = 0.85 * 50 = $42.50
Total Paid without a discount = $50
For water skis:
Total Paid with a 25% discount = 0.75 * (50 + 15) = $44.25
For jewelry:
Total Paid with a 10% discount = 0.90 * (50 - 15) = $31.50
Based on the calculations, I would suggest that Winona and Takoda buy their mother the set of power tools. The total cost of the power tools is $50, and since there is no discount for this present, they only have to pay the full price. The water skis have a 25% discount, but the jewelry has a 10% discount. In terms of cost, the power tools would be the most expensive option, but it would be a gift that their mother might find more useful and long-lasting compared to water skis or jewelry.
To show how much Winona and Takoda would pay in total for the power tools, we can use two expressions:
1. The initial cost of power tools: d dollars
2. The total amount paid after a 15% discount: d - 0.15d
The expression 0.90(d - 5) refers to the total amount paid after a 10% discount (which is equivalent to getting 90% of the original price) on an item costing (d - 5) dollars. We know this because it is stated that the expression refers to the jewelry option, which has a discount of 10% off the original price.
This expression could also be written as (0.90d - 0.90*5) or as 0.9d - 4.5.
Let's choose d = $50 as a value between $25 and $100 to calculate the total cost of each possible present:
1. Power tools: The total amount paid for power tools would be 50 - 0.15*50 = $42.50.
2. Water skis: The total amount paid for water skis would be 50 + 15 - 25%*(50 + 15) = $55.50.
3. Jewelry: The total amount paid for jewelry would be 0.90(50 - 15) = $31.50.
Based on these calculations, Winona and Takoda should buy the jewelry since it has the lowest total cost of $31.50. Additionally, the expression for the total amount paid for the jewelry indicates that a 10% discount is applied to the original price (d - 15 dollars). Therefore, by getting the jewelry, they can save the most money compared to the other options.
To find the total cost if Winona and Takoda bought their mother the set of power tools, we can use the expression (1 - discount%) * cost of power tools. Here, the cost of the power tools is represented by 'd' dollars, and the discount is 15%.
Expression 1: 0.85d (Power tools cost with discount)
Another expression to show how much Winona and Takoda would pay in total can be found by adding the initial cost 'd' with the discount amount (15% of d).
Expression 2: d + (0.15d) = 1.15d (Power tools cost with discount)
The expression 0.90(d - 5) refers to the cost of a different present where the original cost 'd' is reduced by $5 and then multiplied by 0.90, which represents a 10% discount. The expression 0.90(d - 5) can be simplified as 0.90d - 4.5.
To choose a value for 'd' between $25 and $100, let's assume d = $50.
For the power tools:
Expression 1: 0.85 * 50 = $42.50
Expression 2: 1.15 * 50 = $57.50
For the water skis:
Cost = 50 + 15 = $65
Discount = 0.75 * 65 = $48.75 (25% discount)
Total Paid = 65 - 48.75 = $16.25
For the jewelry:
Cost = 50 - 15 = $35
Discount = 0.90 * 35 = $31.50 (10% discount)
Total Paid = 35 - 31.50 = $3.50
Based on these calculations, Winona and Takoda should buy their mother the set of power tools for $42.50. It has the lowest total cost among the options, making it the most economical choice for them.