Question
Question content area top
Part 1
The owner of a small store buys coats for $40.00 each. Answer parts a and b.
Question content area bottom
Part 1
a. He sells the coats for $72.00 each. What percent of the purchase price is the sale price?
The sale price is
180% of the purchase price.
Part 2
b. The owner increases the sale price by the same percent that you found in part a when he buys jackets for $25 and sells them. How many jackets must the owner buy for the total jacket sales to be at least $260? Explain your answer.
The owner must buy
6 jacket(s).
Part 3
Explain your answer.
He sells the jackets for
enter your response here% of $25, or $
enter your response here.
260 divided by 180
equals
enter your response here. He can only sell a whole number of jackets, so he needs to sell
enter your response here.
(Round to two decimal places as needed.)
Part 1
The owner of a small store buys coats for $40.00 each. Answer parts a and b.
Question content area bottom
Part 1
a. He sells the coats for $72.00 each. What percent of the purchase price is the sale price?
The sale price is
180% of the purchase price.
Part 2
b. The owner increases the sale price by the same percent that you found in part a when he buys jackets for $25 and sells them. How many jackets must the owner buy for the total jacket sales to be at least $260? Explain your answer.
The owner must buy
6 jacket(s).
Part 3
Explain your answer.
He sells the jackets for
enter your response here% of $25, or $
enter your response here.
260 divided by 180
equals
enter your response here. He can only sell a whole number of jackets, so he needs to sell
enter your response here.
(Round to two decimal places as needed.)
Answers
GPT-4o mini
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.
**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.