Let's break down the parts as requested.
Part 1
a. What percent of the purchase price is the sale price?
The purchase price of the coat is $40.00, and the sale price is $72.00.
To find what percent the sale price is of the purchase price, you can use the formula:
\[ \text{Percent} = \left( \frac{\text{Sale Price}}{\text{Purchase Price}} \right) \times 100 \]
So,
\[ \text{Percent} = \left( \frac{72.00}{40.00} \right) \times 100 = 1.8 \times 100 = 180% \]
Part 2
b. How many jackets must the owner buy for the total jacket sales to be at least $260?
First, we need to calculate the new sale price for jackets based on the previous percentage increase (180%).
The purchase price of the jackets is $25.00. To find the sale price:
\[ \text{Sale Price} = \text{Purchase Price} \times \left( 1 + \frac{180}{100} \right) = 25 \times 1.8 = 45.00 \]
Next, we need to find out how many jackets must be sold to make at least $260 in sales.
Let \( x \) be the number of jackets sold. The equation would be:
\[ 45x \geq 260 \]
Now, solving for \( x \):
\[ x \geq \frac{260}{45} \approx 5.78 \]
Since the owner can only sell whole jackets, he must round up:
\[ x = 6 \]
So, he must buy 6 jackets.
Part 3
Explain your answer.
The owner sells the jackets for \( 180% \) of the purchase price of $25.00, which calculates to:
\[ \text{Selling Price of Jackets} = 1.8 \times 25 = 45.00 \]
To ensure total sales of at least $260:
We calculated that:
\[ 260 \div 45 = 5.78 \]
Since the owner can't sell a fraction of a jacket, he rounds up to 6 jackets to meet the sales goal of at least $260.
So in summary:
- He sells the jackets for 180% of $25, or $45.00.
- He needs to sell at least 6 jackets to reach a total of at least $260.
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