To determine the smallest sale rate that Kedwin needs to afford the headphones, we need to calculate the total cost of the headphones including shipping and then find the necessary sale percentage.
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Calculate the total cost including shipping: The cost of the headphones is $175.00. The shipping is 10% of this cost.
\[ \text{Shipping} = 10% \times 175 = 0.10 \times 175 = 17.50 \]
\[ \text{Total cost} = 175 + 17.50 = 192.50 \]
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Determine how much Kedwin can afford: Kedwin has $150.00.
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Find the needed sale price to make it affordable:
Let \( x \) be the sale percentage (as a decimal). The sale price can be calculated using:\[ \text{Sale Price} = 175 \times (1 - x) \]
Adding the shipping, the equation becomes:
\[ \text{Total Cost with Sale} = 175 \times (1 - x) + 17.50 \]
We need to set this less than or equal to $150.00:
\[ 175 \times (1 - x) + 17.50 \leq 150 \]
Subtract 17.50 from both sides:
\[ 175 \times (1 - x) \leq 150 - 17.50 \]
\[ 175 \times (1 - x) \leq 132.50 \]
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Solve for \( x \):
Divide both sides by 175:
\[ 1 - x \leq \frac{132.50}{175} \]
Calculate the fraction:
\[ \frac{132.50}{175} = 0.757142857 \ldots \approx 0.7571 \]
So we have:
\[ 1 - x \leq 0.7571 \]
Rearranging gives:
\[ x \geq 1 - 0.7571 = 0.2429 \]
Converting to a percentage:
\[ x \geq 24.29% \]
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Determine the smallest sale rate option:
The closest option is 25%.
Thus, the smallest sale rate that Kedwin needs to be able to afford the headphones is 25%.