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Let's go through each part of this problem.

### Part (a)
The owner buys coats for $40 each and sells them for $72 each. The question asks for the percentage of the purchase price that the sale price represents.

1. **Calculate the percentage increase from $40 to $72:**

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

   Plugging in the values:

   \[
   \left( \frac{72 - 40}{40} \right) \times 100 = \left( \frac{32}{40} \right) \times 100 = 80\%
   \]

   So, the sale price is **180%** of the purchase price (100% + 80%).

### Part (b)
The owner increases the sale price by the same percentage (80%) each time they buy jackets for $25 and sells them. We need to find how many jackets the owner must sell for the total sales to be at least $260.

1. **Calculate the new sale price per jacket:**
   
   The purchase price for each jacket is $25, and the sale price is increased by 80%. So:

   \[
   \text{Sale Price} = 25 \times 1.80 = 45
   \]

2. **Set up an inequality to find the minimum number of jackets:**

   Let $ x $ be the number of jackets. The total revenue must be at least $260, so:

   \[
   45x \geq 260
   \]

   Solve for $ x $:

   \[
   x \geq \frac{260}{45} \approx 5.78
   \]

   Since the number of jackets must be a whole number, the owner needs to buy **6 jackets** to reach at least $260 in sales.

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Would you like more details on any part of the solution?

### Related Questions
1. What would the required sale price be if the markup percentage was only 50%?
2. How much total profit would the owner make if they sold exactly 6 jackets?
3. What if the cost per jacket increased to $30 with the same markup?
4. How many jackets would the owner need to sell to make $300 in sales?
5. If the markup changed to 100%, how would this affect the sale price?

### Tip
When calculating percentage increases, always add 100% to the markup to find the new sale price as a percentage of the original price.

The owner of a small store buys coats for $40.00 each. Answer parts a and b:

(a) She sells the coats for $72.00 each. What percent of the purchase price is the sale price?
(b) The owner increases the sale price by the same percent that you found in part a when she buys jackets for $25 and sells them. How many jackets must the owner buy for the total jacket sales to be at least $260?

Learn how to calculate the percentage increase in price for coats sold by a store owner and determine the minimum number of jackets needed to achieve a revenue target. This problem includes key math concepts such as percentages and inequalities, suitable for Grade 7 students.

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