Let's break down each part of the question step by step.

---

a. Clearance Price:

• Cost per set: $580
• Markup: 50% of the cost

To calculate the regular selling price, we need to add the markup to the cost: $\text{Regular Price} = \text{Cost} + (\text{Markup Percentage} \times \text{Cost})$ $\text{Regular Price} = 580 + (0.50 \times 580)$ $\text{Regular Price} = 580 + 290 = 870$

Now, to calculate the clearance price, we apply a 30% markdown from the regular price: $\text{Clearance Price} = \text{Regular Price} - (\text{Markdown Percentage} \times \text{Regular Price})$ $\text{Clearance Price} = 870 - (0.30 \times 870)$ $\text{Clearance Price} = 870 - 261 = 609$

So, the clearance price is $609.

---

b. Rate of Markdown to Sell at Cost:

We are looking for the markdown rate to sell the set at cost ($580). The regular price was $870, and the cost is $580.

To find the markdown percentage, we first calculate the difference between the regular price and the cost: $\text{Markdown Amount} = \text{Regular Price} - \text{Cost}$ $\text{Markdown Amount} = 870 - 580 = 290$

Now, to calculate the markdown rate (as a percentage of the regular price), we divide the markdown amount by the regular price and multiply by 100: $\text{Markdown Rate} = \left( \frac{\text{Markdown Amount}}{\text{Regular Price}} \right) \times 100$ $\text{Markdown Rate} = \left( \frac{290}{870} \right) \times 100 \approx 33.3\%$

So, the markdown rate is 33.3%.

---

Summary:

a. Clearance Price = $609

b. Markdown Rate = 33.3%

---

Would you like more details on any part of this, or do you have any further questions? Here are some follow-up questions to explore:

1. How do you calculate percentage markups and markdowns for other retail scenarios?
2. What are some common strategies retailers use for pricing and clearance sales?
3. How does cost structure affect pricing decisions in retail?
4. How do businesses decide on the level of markdown to apply during clearance?
5. What factors contribute to setting a markup percentage, and how is it determined?

Tip: In retail pricing, understanding your markup and markdown strategies helps balance profits while staying competitive in the market!