A CD was marked down 10% during a yearend sale. The record outlet paid 200 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?

To solve this problem, we need to find:

1. The regular selling price (before discount).
2. The sale price (after the 10% discount).
3. The profit or loss.

Let's break this down step-by-step.

### Step 1: Understanding the Variables

- **Cost Price (C):** The outlet paid 200 for the CD.
- **Expenses (E):** 15% of the selling price.
- **Profit (P):** 12% of the selling price.
- **Discount:** 10% off the regular selling price.
  
### Step 2: Express the Profit Formula
The total profit is 12% of the selling price, which can be written as:
\[
\text{Profit} = 0.12 \times \text{Selling Price} 
\]

The profit is also the difference between the selling price and the cost price, factoring in the expenses:
\[
\text{Profit} = \text{Selling Price} - \text{Expenses} - \text{Cost Price}
\]

Since the expenses are 15% of the selling price, we express it as:
\[
\text{Expenses} = 0.15 \times \text{Selling Price}
\]

Substitute these into the profit equation:
\[
0.12 \times \text{Selling Price} = \text{Selling Price} - 0.15 \times \text{Selling Price} - 200
\]

### Step 3: Solve for the Regular Selling Price (S)
Rearranging the equation:
\[
0.12 \times \text{Selling Price} = (1 - 0.15) \times \text{Selling Price} - 200
\]
\[
0.12 \times \text{Selling Price} = 0.85 \times \text{Selling Price} - 200
\]
\[
0.12 \times \text{Selling Price} - 0.85 \times \text{Selling Price} = -200
\]
\[
-0.73 \times \text{Selling Price} = -200
\]
\[
\text{Selling Price} = \frac{200}{0.73}
\]
Now, let’s calculate this value.

### Step 4: Find the Sale Price
Once we have the regular selling price, we apply the 10% discount to find the sale price.

\[
\text{Sale Price} = \text{Regular Selling Price} \times (1 - 0.10)
\]

### Step 5: Calculate Profit or Loss
Finally, we determine if there's a profit or loss based on the selling price and cost price.

Let me calculate these values now.### Solution:

1. **Regular Selling Price:** The regular selling price of the CD is approximately 273.97.
2. **Sale Price:** After the 10% discount, the sale price of the CD is approximately 246.58.
3. **Profit or Loss:** The outlet makes a profit of approximately 46.58 when the CD is sold at the discounted price.

Would you like more details, or do you have any questions?

Here are 5 related questions you could explore:
1. What would happen to the profit if the expenses increased to 20% of the selling price?
2. How much would the selling price need to be to break even with no profit or loss?
3. What would the sale price be with a different discount, say 15% instead of 10%?
4. How much additional profit could be earned if the discount were reduced to 5%?
5. How would a 20% profit margin impact the regular selling price?

**Tip:** Always recheck profit or loss calculations when discounts and expenses are involved to ensure accurate business decisions.

A CD was marked down 10% during a year-end sale. The record outlet paid 200 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?

Find the regular selling price, sale price, and profit for a CD marked down 10% during a sale. This detailed solution covers algebraic concepts and percentage calculations, making it suitable for students in Grades 9-10.

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