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.)

Answer 1

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.