A clothing merchant purchases a shipment of clothes for $37,000.00 with discounts of 8.00% and 4.00%. He sells it to a customer at a price which includes 21.00% profit on selling price and overhead expenses of 25.00% on selling price.

a. How müch did it cost him to purchase the container of clothes?

$0.00

Round to the nearest cent

b. What was the selling price of the container of clothes?

$0.00

Round to the nearest cent

To solve this problem, we need to break it down into two parts:

### Part (a): Cost of Purchasing the Container of Clothes

The merchant receives two successive discounts of 8.00% and 4.00% on the original price of $37,000.00.

1. **First Discount:**
   \[
   \text{First Discount Amount} = 0.08 \times 37,000 = 2,960.00
   \]
   \[
   \text{Price after First Discount} = 37,000 - 2,960 = 34,040.00
   \]

2. **Second Discount:**
   \[
   \text{Second Discount Amount} = 0.04 \times 34,040 = 1,361.60
   \]
   \[
   \text{Price after Second Discount} = 34,040 - 1,361.60 = 32,678.40
   \]

So, the cost to purchase the container of clothes is **$32,678.40**.

### Part (b): Selling Price of the Container of Clothes

We need to find the selling price which includes a profit of 21.00% on the selling price and overhead expenses of 25.00% on the selling price.

1. **Define Variables:**
   - Let $ SP $ be the selling price.
   - The cost price (CP) is $32,678.40.

2. **Selling Price Formula:**
   - The profit is 21% of the selling price:
     \[
     \text{Profit} = 0.21 \times SP
     \]
   - The overhead expenses are 25% of the selling price:
     \[
     \text{Overhead Expenses} = 0.25 \times SP
     \]
   - The total cost includes the cost price, profit, and overhead expenses:
     \[
     \text{Cost Price} = CP = SP - \text{Profit} - \text{Overhead Expenses}
     \]
     \[
     32,678.40 = SP - 0.21 \times SP - 0.25 \times SP
     \]
     \[
     32,678.40 = SP (1 - 0.21 - 0.25)
     \]
     \[
     32,678.40 = SP \times 0.54
     \]

3. **Solve for Selling Price:**
   \[
   SP = \frac{32,678.40}{0.54} = 60,518.52
   \]

So, the selling price of the container of clothes is **$60,518.52**.

Would you like further details or have any questions?

Here are 8 related questions for further exploration:

1. How would the calculations change if there were additional discounts applied?
2. How do different profit margins impact the final selling price?
3. What factors should be considered when setting a selling price?
4. How can overhead expenses be minimized to increase profit?
5. What are the implications of discount strategies on business revenue?
6. How to calculate the break-even point in such transactions?
7. What are the benefits of offering successive discounts to customers?
8. How to factor in taxes when calculating the selling price?

**Tip:** When calculating multiple successive discounts, always apply each discount to the price resulting from the previous discount, not to the original price.

Learn how to calculate the cost price and selling price of a shipment of clothes after successive discounts and including overhead expenses. This problem involves percentage calculations and profit margin considerations. Suitable for high school students.

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