. A CD was marked down 10% during a yearend sale. The record outlet paid P200 for that CD and the expenses are 15% of the selling price. To a achieve a profit of 12% of the selling price what was the regular selling price? What was its sale price? How much is the profit or loss?

Let's define the terms and solve the problem step by step:

- The cost price of the CD is P200.
- The store incurs expenses that are 15% of the selling price (let's call this selling price \( S \)).
- The store wants a profit of 12% of the selling price.

We are asked to find:
1. The regular selling price \( S \) before the 10% markdown.
2. The sale price after the 10% discount.
3. The profit or loss.

### Step 1: Establishing the relationships

1. **Selling Price and Profit**:
   - Profit is 12% of the selling price. Therefore:
   \[
   \text{Profit} = 0.12S
   \]
   
2. **Expenses**:
   - Expenses are 15% of the selling price. Therefore:
   \[
   \text{Expenses} = 0.15S
   \]
   
3. **Profit Equation**:
   - The total cost to the store includes the expenses and the cost price of the CD:
   \[
   \text{Total Cost to Store} = 200 + 0.15S
   \]
   - The profit is calculated as:
   \[
   \text{Profit} = S - \text{Total Cost to Store}
   \]
   Substituting the total cost:
   \[
   \text{Profit} = S - (200 + 0.15S)
   \]
   Since profit is 12% of the selling price:
   \[
   0.12S = S - (200 + 0.15S)
   \]
   
4. **Solving for \( S \)**:
   Let's simplify and solve the equation:
   \[
   0.12S = S - 200 - 0.15S
   \]
   Combine like terms:
   \[
   0.12S + 0.15S = S - 200
   \]
   \[
   0.27S = S - 200
   \]
   Subtract \( 0.27S \) from both sides:
   \[
   0.73S = 200
   \]
   Solve for \( S \):
   \[
   S = \frac{200}{0.73} \approx 273.97
   \]
   
So, the regular selling price is approximately **P273.97**.

### Step 2: Sale Price After 10% Markdown

The sale price is 10% off the regular selling price:
\[
\text{Sale Price} = S - 0.10S = 0.90S
\]
Substitute \( S = 273.97 \):
\[
\text{Sale Price} = 0.90 \times 273.97 \approx 246.57
\]

So, the sale price is approximately **P246.57**.

### Step 3: Profit or Loss

Since the store paid P200 for the CD and we already know that the expenses are 15% of the selling price:

For the **sale price**:
1. **Expenses** at sale price: 
   \[
   \text{Expenses} = 0.15 \times 246.57 \approx 36.99
   \]
2. **Total cost to store at sale price**:
   \[
   \text{Total Cost} = 200 + 36.99 = 236.99
   \]
3. **Profit or Loss at sale price**:
   \[
   \text{Profit/Loss} = 246.57 - 236.99 \approx 9.58
   \]

Therefore, the profit at the sale price is approximately **P9.58**.

---

### Final Answers:
1. Regular selling price: **P273.97**.
2. Sale price: **P246.57**.
3. Profit at the sale price: **P9.58**.

Would you like more details or clarification on any part?

### Relative Questions:
1. How do you calculate a percentage discount on a selling price?
2. What is the formula to calculate profit percentage?
3. How do expenses affect the selling price and profit margins?
4. How do markdowns influence the overall profitability of a product?
5. Can the profit still be positive even after applying a discount?

### Tip:
Always account for both direct costs (like the purchase price) and indirect costs (like expenses) when calculating profit.

A CD was marked down 10% during a yearend sale. The record outlet paid P200 for that CD and the expenses are 15% of the selling price. To achieve a profit of 12% of the selling price, what was the regular selling price? What was its sale price? How much is the profit or loss?

Learn how to calculate the regular selling price, sale price, and profit of a CD with a 10% discount. This detailed solution includes key concepts like profit, expenses, and percentage calculations, ideal for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation