Let’s break down the problem step by step.

Definitions:

• Cost price (C): ₱200 (this is the amount the record outlet paid for the CD).
• Expenses: 15% of the selling price.
• Desired profit: 12% of the selling price.
• Sale discount: 10% markdown during the year-end sale.

Step 1: Establish the Regular Selling Price (R)

We need to find the regular selling price (R) so that after covering both expenses and the desired profit, the selling price meets the requirements.

Expenses:

• Expenses = 15% of $R$ = $0.15R$.

Profit:

• Desired profit = 12% of $R$ = $0.12R$.

The total cost to the seller is the sum of the cost price (₱200) and expenses. This total should also be less than the selling price by the amount of the profit, so:

$\text{Total Cost} = \text{Cost Price} + \text{Expenses} = 200 + 0.15R$

We also know that the profit is 12% of $R$, which means:

$\text{Total Cost} = \text{Selling Price} - \text{Profit} = R - 0.12R$

Thus:

$200 + 0.15R = R - 0.12R$

Simplifying the equation:

$200 + 0.15R = 0.88R$

Step 2: Solve for $R$

$0.88R - 0.15R = 200$ $0.73R = 200$ $R = \frac{200}{0.73} \approx 273.97$

So, the regular selling price (R) is approximately ₱273.97.

Step 3: Calculate the Sale Price

During the sale, there’s a 10% discount. The sale price (S) is:

$S = R - 0.10R = 0.90R$ $S = 0.90 \times 273.97 \approx 246.57$

So, the sale price is approximately ₱246.57.

Step 4: Calculate Profit or Loss

The cost price is ₱200, and the expenses are 15% of the selling price (R).

$\text{Expenses} = 0.15 \times 273.97 \approx 41.10$

So, the total cost to the seller is:

$\text{Total Cost} = 200 + 41.10 = 241.10$

The profit at the regular price is:

$\text{Profit at regular price} = R - \text{Total Cost} = 273.97 - 241.10 \approx 32.87$

This is a profit.

However, if the CD is sold at the sale price (₱246.57), the profit or loss is:

$\text{Profit at sale price} = 246.57 - 241.10 \approx 5.47$

So, at the sale price, there is still a profit of ₱5.47.

Summary:

• Regular Selling Price: ₱273.97
• Sale Price: ₱246.57
• Profit at Regular Price: ₱32.87
• Profit at Sale Price: ₱5.47

Do you want more details or have any questions?

Here are 5 related questions:

1. How would the selling price change if the desired profit margin was 20% instead of 12%?
2. How do the expenses affect the profit calculation?
3. What would happen if the cost price of the CD increased to ₱250?
4. How would the final selling price change with a 20% discount instead of 10%?
5. What is the minimum selling price to avoid a loss if expenses are 15% of the price?

Tip: When calculating profit, always factor in expenses to ensure that your selling price not only covers costs but also provides the desired profit margin.