A store purchases camcorders for $500 each. Its overhead expenses are 15% of the cost and it wants an operating profit of $250 on the sale of each camcorder. The store cannot sell their camcorders at regular selling price and markdown the price by $100. Calculate the rate of markdown and the reduced selling price.

Let's break this problem down step by step to calculate the **rate of markdown** and the **reduced selling price**.

### Step 1: Calculate Overhead Expenses
The store incurs overhead expenses that are **15%** of the cost price of each camcorder.

- **Cost price of the camcorder = $500**
- **Overhead expenses = 15% of $500**

\[
\text{Overhead expenses} = 0.15 \times 500 = 75
\]

So, the total overhead expenses are **$75**.

### Step 2: Calculate the Target Selling Price
The store wants to make an operating profit of **$250** on each camcorder. The target selling price will be the sum of the **cost price**, **overhead expenses**, and **desired profit**.

- **Cost price = $500**
- **Overhead expenses = $75**
- **Desired profit = $250**

\[
\text{Target Selling Price} = 500 + 75 + 250 = 825
\]

So, the regular selling price is **$825**.

### Step 3: Calculate the Reduced Selling Price
The store marks down the camcorder by **$100**, so the reduced selling price is:

\[
\text{Reduced Selling Price} = 825 - 100 = 725
\]

### Step 4: Calculate the Rate of Markdown
The rate of markdown is the percentage by which the price was reduced compared to the regular selling price.

\[
\text{Rate of Markdown} = \frac{\text{Markdown Amount}}{\text{Original Selling Price}} \times 100
\]

Here, the markdown amount is **$100** and the original selling price is **$825**.

\[
\text{Rate of Markdown} = \frac{100}{825} \times 100 \approx 12.12\%
\]

### Final Answer:
- The **rate of markdown** is approximately **12.12%**.
- The **reduced selling price** is **$725**.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What would happen to the markdown rate if the store marked down the price by $150 instead of $100?
2. How much profit would the store make if it sold the camcorder at the reduced price of $725?
3. What would the rate of markdown be if the store increased overhead expenses to 20%?
4. If the cost price of the camcorder changed to $600, how would that affect the selling price and markdown rate?
5. What is the minimum price the store could sell the camcorder at and still cover its overhead and desired profit?

**Tip**: When calculating markdown percentages, always remember to divide the markdown amount by the original price, not the new price.

Learn how to calculate the rate of markdown and reduced selling price for camcorders purchased at $500 with overhead expenses and desired profit. This step-by-step guide covers cost, profit, and markdown rate calculations, suitable for students in Grades 8-10.

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