A store in Vancouver has operating expenses of 15% of the selling price and the operating profit is 20% of the selling price. During a sale, their watches were marked down by 30%. What is the profit or loss at the sale price if they purchased the watches at $597 each?
Express the answer as a positive number for profit and negative number for loss, rounded to the nearest cent

To determine the profit or loss at the sale price, we can break down the problem into steps:

1. **Calculate the original selling price**:
   - Let the original selling price be $ S $.
   - The operating profit is 20% of the selling price: $ 0.20S $.
   - The operating expenses are 15% of the selling price: $ 0.15S $.
   - Therefore, the store's cost to purchase the watches, which includes both the expenses and profit, can be expressed as:
     \[
     \text{Cost} + 0.15S + 0.20S = S
     \]
     \[
     \text{Cost} = S - 0.35S = 0.65S
     \]
   - The store's cost of purchasing the watches $ \text{Cost} $ is given as $597, so:
     \[
     0.65S = 597
     \]
     \[
     S = \frac{597}{0.65} = 918.46
     \]

2. **Determine the sale price**:
   - During the sale, the watches were marked down by 30%:
     \[
     \text{Sale Price} = S - 0.30S = 0.70S
     \]
     \[
     \text{Sale Price} = 0.70 \times 918.46 = 642.92
     \]

3. **Calculate the profit or loss**:
   - The profit or loss is determined by subtracting the purchase cost from the sale price:
     \[
     \text{Profit or Loss} = \text{Sale Price} - \text{Cost}
     \]
     \[
     \text{Profit or Loss} = 642.92 - 597 = 45.92
     \]

Since the result is positive, this indicates a profit.

**Final Answer**: The profit at the sale price is **$45.92**.

Would you like more details or have any questions?

Here are 8 related questions that expand on this problem:

1. How would the profit change if the markdown was 40% instead of 30%?
2. What would the operating expenses be at the sale price?
3. How does the initial markup percentage relate to the final profit?
4. If the store wanted a profit of $100 at the sale price, what should the original selling price be?
5. What if the purchase cost was $700, what would the profit or loss be at the sale price?
6. How would the calculation change if the operating expenses were 20% of the selling price?
7. Can you determine the break-even sale price given the same purchase cost and expenses?
8. What is the percentage profit based on the purchase cost?

**Tip**: When dealing with percentage problems, always define your base values clearly to avoid confusion in calculations.

Explore how to calculate profit or loss when watches are marked down by 30% during a sale in Vancouver. Understand the impact of operating expenses and operating profit percentages on the final financial outcome. Detailed step-by-step solution provided.

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