https://file.aiquickdraw.com/mathbot/file/172843628558425oabu61.jpg

Let's break down the steps to solve the given problems:

### Problem 6:
We are given:
- **Case Cost**: This is the cost of an entire case.
- **Packages per Case**: Number of individual packages in the case.
- **Markup Rate Based on Selling Price**: This is the percentage markup that the store applies to set the **Regular Selling Price**.

The regular selling price of each package is computed using the formula:

\[
\text{Regular Selling Price per Package} = \frac{\text{Case Cost}}{\text{Packages per Case}} \times \left(1 + \frac{\text{Markup Rate}}{100}\right)
\]

Once we have the regular selling price per package, we will reduce it by 25% for the sale price. The sale price is given by:

\[
\text{Sale Price} = \text{Regular Selling Price} \times (1 - 0.25)
\]

Let’s compute the **Regular Selling Price** and **Sale Price** for each item:

1. **Butter-top dinner rolls**:
   - Case Cost: \$9.48
   - Packages per Case: 12
   - Markup Rate: 25%

   \[
   \text{Regular Selling Price} = \frac{9.48}{12} \times \left(1 + \frac{25}{100}\right) = 0.79 \times 1.25 = 0.99
   \]
   \[
   \text{Sale Price} = 0.99 \times (1 - 0.25) = 0.74
   \]

2. **Crescent dinner rolls**:
   - Case Cost: \$14.88
   - Packages per Case: 12
   - Markup Rate: 29%

   \[
   \text{Regular Selling Price} = \frac{14.88}{12} \times \left(1 + \frac{29}{100}\right) = 1.24 \times 1.29 = 1.60
   \]
   \[
   \text{Sale Price} = 1.60 \times (1 - 0.25) = 1.20
   \]

3. **Banana bread**:
   - Case Cost: \$23.52
   - Packages per Case: 12
   - Markup Rate: 30%

   \[
   \text{Regular Selling Price} = \frac{23.52}{12} \times \left(1 + \frac{30}{100}\right) = 1.96 \times 1.30 = 2.55
   \]
   \[
   \text{Sale Price} = 2.55 \times (1 - 0.25) = 1.91
   \]

4. **Apricot nut bread**:
   - Case Cost: \$26.82
   - Packages per Case: 9
   - Markup Rate: 29%

   \[
   \text{Regular Selling Price} = \frac{26.82}{9} \times \left(1 + \frac{29}{100}\right) = 2.98 \times 1.29 = 3.84
   \]
   \[
   \text{Sale Price} = 3.84 \times (1 - 0.25) = 2.88
   \]

5. **Cranberry nut muffins**:
   - Case Cost: \$21.12
   - Packages per Case: 8
   - Markup Rate: 30%

   \[
   \text{Regular Selling Price} = \frac{21.12}{8} \times \left(1 + \frac{30}{100}\right) = 2.64 \times 1.30 = 3.43
   \]
   \[
   \text{Sale Price} = 3.43 \times (1 - 0.25) = 2.57
   \]

### Problem 7:
We are given:
- Sale price: \$11.98
- Markdown rate: 60%

Let the regular selling price be $x$. After a markdown of 60%, the sale price is given by:

\[
\text{Sale Price} = x \times (1 - 0.60)
\]

Solving for $x$:

\[
11.98 = x \times 0.40
\]
\[
x = \frac{11.98}{0.40} = 29.95
\]

Thus:
- **Regular Selling Price** = \$29.95
- **Markdown** = $29.95 - 11.98 = 17.97$

---

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

### Follow-up Questions:
1. How do we calculate markup based on cost instead of selling price?
2. What is the relationship between markup percentage and profit?
3. How do markdowns affect profit margins for stores?
4. How would the sale price change if the discount was 30% instead of 25%?
5. What is the effect of increasing the packages per case on the price per package?

### Tip:
Understanding markup is crucial in pricing strategies as it determines the final retail price while considering cost and profitability.

Dottie Hanlen works for Delta Grocery Store. She has been asked to price some packages of frozen foods based on the given case cost, number of packages per case, and markup rate. Calculate the regular selling price and the sale price after a 25% storewide promotion for each item.

Learn how to calculate the regular selling price and sale price of frozen foods based on case cost, number of packages, and markup rate. This problem covers essential concepts in percentages and discounts, suitable for students in Grade 10-12.

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