Question

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
  
enter your response here ​jacket(s).

Answer 1

To solve the problem, we'll tackle each part step by step.

### Part 1: Finding the Sale Price as a Percentage of the Purchase Price

1. **Calculate the sale price percentage relative to the purchase price.**
- Purchase Price of Coat = $40.00
- Sale Price of Coat = $72.00

To find what percent the sale price is of the purchase price:

\[
\text{Percentage} = \left( \frac{\text{Sale Price}}{\text{Purchase Price}} \right) \times 100
\]

Substituting the values:

\[
\text{Percentage} = \left( \frac{72}{40} \right) \times 100 = 1.8 \times 100 = 180\%
\]

**The sale price is 180% of the purchase price.**

### Part 2: Jacket Sales

1. **Determine the increase percentage based on the coats' pricing.**
- Since we found that the sale price of the coats is 180% of the purchase price, that means the increase is 80% of the purchase price (because 180% - 100% = 80%).

2. **Calculate the increased sale price for the jackets.**
- Purchase Price of Jacket = $25.00
- Increase = 80% of $25.00

First, calculate 80% of $25.00:

\[
\text{Increase} = 0.80 \times 25 = 20
\]

Now, we find the new sale price of the jackets:

\[
\text{New Sale Price} = \text{Purchase Price} + \text{Increase} = 25 + 20 = 45
\]

So, the sale price of the jackets is $45.00 each.

3. **Determine how many jackets are needed to achieve at least $260 in sales.**

To find out how many jackets the owner must sell to reach at least $260:

\[
\text{Number of Jackets} = \left\lceil \frac{\text{Total Sales Goal}}{\text{Sale Price per Jacket}} \right\rceil
\]

Substituting in the values:

\[
\text{Number of Jackets} = \left\lceil \frac{260}{45} \right\rceil \approx \left\lceil 5.78 \right\rceil
\]

Hence, rounding up, the owner needs to sell **6 jackets** to at least meet the sales goal of $260.

### Final Answers

Part 1: The sale price is **180%** of the purchase price.
Part 2: The owner must buy **6 jackets**.