6. 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?

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

### Step 1: Define the variables
- Let \( x \) be the **regular selling price** of the CD (before the discount).
- The **record outlet paid** 200 for the CD.
- **Expenses** are 15% of the selling price, which is \( 0.15x \).
- The CD was **marked down by 10%** during the sale, so the **sale price** is \( 0.90x \).
- The desired **profit** is 12% of the selling price, or \( 0.12x \).

### Step 2: Set up the profit equation
The **profit** is the difference between the **selling price** and the **costs** (which include both the expense and the cost price of the CD). The desired profit should be 12% of the selling price.

\[
\text{Profit} = \text{Selling Price} - (\text{Cost Price} + \text{Expenses})
\]

Substitute the values:
\[
0.12x = x - (200 + 0.15x)
\]

### Step 3: Solve for the regular selling price \( x \)
Simplify the equation:
\[
0.12x = x - 200 - 0.15x
\]

Combine like terms:
\[
0.12x + 0.15x = x - 200
\]
\[
0.27x = x - 200
\]

Subtract \( 0.27x \) from both sides:
\[
0.73x = 200
\]

Solve for \( x \):
\[
x = \frac{200}{0.73} \approx 273.97
\]

So, the **regular selling price** is approximately **273.97**.

### Step 4: Calculate the sale price
The CD was marked down by 10%, so the sale price is:
\[
\text{Sale Price} = 0.90x = 0.90 \times 273.97 \approx 246.57
\]

Thus, the **sale price** is approximately **246.57**.

### Step 5: Calculate the profit or loss during the sale
To find the profit or loss, we need to compare the sale price with the costs (expenses + cost price).

Expenses during the sale are:
\[
\text{Expenses} = 0.15 \times \text{Sale Price} = 0.15 \times 246.57 \approx 36.99
\]

Total cost = \( 200 + 36.99 = 236.99 \).

The profit (or loss) is the difference between the sale price and the total cost:
\[
\text{Profit or Loss} = 246.57 - 236.99 = 9.58
\]

Thus, there is a **profit of 9.58** during the sale.

### Summary of Results:
- **Regular selling price**: 273.97
- **Sale price**: 246.57
- **Profit during the sale**: 9.58

Would you like any further details on any of these steps?

### Additional Questions:
1. What would the selling price need to be to achieve a 20% profit instead?
2. How would the results change if the markdown was 15% instead of 10%?
3. What is the profit percentage during the sale compared to the cost price?
4. How do the expenses affect the overall profit calculation?
5. What if the record outlet paid a different amount, say 250? How would the prices change?

### Tip:
In profit problems, always differentiate between profit as a percentage of cost price and profit as a percentage of selling price. They often lead to different results!

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 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?

Calculate the regular and sale price of a CD marked down by 10% during a sale. Given that the store paid 200 for the CD and expenses are 15% of the selling price, learn how to find the profit and solve for the regular selling price. Includes step-by-step breakdown and key formulas.

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