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 find the total paid for the power tools, we need to multiply the cost of the power tools by (1 - discount). So the expression for Winona and Takoda's total paid for the power tools would be:
Total Paid = d * (1 - 0.15) = 0.85d
The expression 0.90(d - 5) refers to the total paid for a present, which originally costs d dollars, but is given a 10% discount and then another $5 off. We know this because the expression is multiplying the original cost (d - 5) by 0.90, which represents the remaining 90% of the cost after the discount.
This expression could also be written as 0.90d - 4.50, if we distribute the 0.90 through.
Let's choose d = $50 as a value.
Total paid for power tools = 0.85 * 50 = $42.50
Total paid for water skis = (50 + 15) * (1 - 0.25) = $48.75
Total paid for jewelry = (50 - 15) * (1 - 0.10) = $31.50
Based on these calculations, Winona and Takoda should buy the jewelry for their mom. It has the lowest total cost of $31.50 compared to $42.50 for the power tools and $48.75 for the water skis.
Please explain how you got it understandingly
Certainly! Let's break down the problem step by step.
1. Expressions for the total paid for power tools:
The cost of the power tools is represented by d dollars. The discount on power tools is given as 15%. To find the total paid, we need to subtract the discount amount from the cost. This is done by multiplying the cost (d) by (1 - discount), which in this case is 1 - 0.15 = 0.85. So, the expression for the total paid for power tools is 0.85d.
2. Explaining the expression 0.90(d - 5):
The expression 0.90(d - 5) refers to the total paid for a present that originally costs d dollars, but is given a 10% discount and then another $5 off. The first part in the expression, (d - 5), represents the original cost minus $5 off. The second part, 0.90, represents the remaining 90% of the cost after the 10% discount. By multiplying the original cost (d - 5) by 0.90, we find the total paid for this present after the discount and additional $5 off.
3. Calculation for total cost:
Let's choose a value for d. In this case, we'll choose d = $50.
To find the total paid for power tools:
Total Paid = 0.85 * 50 = $42.50
To find the total paid for water skis:
Total Paid = (50 + 15) * (1 - 0.25) = $48.75
To find the total paid for jewelry:
Total Paid = (50 - 15) * (1 - 0.10) = $31.50
4. Selecting the best present:
Based on the calculations, the total cost for the power tools is $42.50, for water skis it is $48.75, and for jewelry it is $31.50. Since Winona and Takoda want to find the present with the lowest total cost, they should choose the jewelry for their mom. The jewelry has the lowest cost of $31.50 compared to the other options.
To calculate the total paid for the power tools, we need to use the discount percentage. The first expression would be:
Total Paid = (Cost of Power tools) - (Discount)
Since the cost of power tools is represented as 'd' dollars and the discount is 15%, the expression becomes:
Total Paid = d - (0.15 * d)
This can also be simplified as:
Total Paid = d(1 - 0.15)
Total Paid = 0.85d
Now, let's analyze the expression 0.90(d - 5). The expression represents the total paid for an item after a discount of 10% has been applied. We know this because the expression involves subtracting 5 from d and then multiplying by 0.90, which is equivalent to a 10% discount.
The expression can also be written as:
Total Paid = d(1 - 0.10)(0.90)
Total Paid = 0.9d - (0.1 * d)
Total Paid = 0.9d - 0.1d
Total Paid = 0.8d
Now let's choose a value for d that is greater than $25 and less than $100. Let's say d = $50.
For power tools: Total Paid = 0.85 * 50 = $42.50
For water skis: Total Paid = (50 + 15) * 0.75 = $48.75
For jewelry: Total Paid = (50 - 15) * 0.90 = $31.50
Based on these calculations, I would recommend Winona and Takoda to buy the jewelry as a present for their mom. The total cost for jewelry is the lowest among the available options, costing only $31.50.