A department store paid ​$37.52 for a wine set. Overhead expense is 14 % of the regular selling price and profit is 10 % of the regular selling price. During a clearance​ sale, the set was sold at a markdown of 18 %. What was the operating profit or loss on the​ sale?

We are given:

- The department store paid $37.52 for a wine set.
- Overhead expense is 14% of the regular selling price.
- Profit is 10% of the regular selling price.
- During the clearance sale, the set was sold at an 18% markdown on the regular selling price.

Let's break down the problem to find the operating profit or loss.

### Step 1: Define the regular selling price
Let the **regular selling price** be $ x $.

- **Overhead expense** = 14% of $ x $ = $ 0.14x $
- **Profit** = 10% of $ x $ = $ 0.10x $

This means the total cost to the store (including the price they paid for the set and overhead expense) is:

\[
\text{Total Cost to Store} = 37.52 + 0.14x
\]

The regular selling price $ x $ can also be represented by:

\[
x = \text{Total Cost to Store} + \text{Profit} = 37.52 + 0.14x + 0.10x
\]

This simplifies to:

\[
x = 37.52 + 0.24x
\]

Solving for $ x $:

\[
x - 0.24x = 37.52
\]
\[
0.76x = 37.52
\]
\[
x = \frac{37.52}{0.76} = 49.37
\]

So, the regular selling price is **$49.37**.

### Step 2: Find the clearance sale price
The wine set was sold at an 18% markdown. The clearance sale price is:

\[
\text{Sale Price} = x - 0.18x = (1 - 0.18) \times 49.37 = 0.82 \times 49.37 = 40.48
\]

### Step 3: Calculate operating profit or loss
The store’s total cost (including overhead) is:

\[
\text{Total Cost to Store} = 37.52 + 0.14 \times 49.37 = 37.52 + 6.91 = 44.43
\]

The operating profit or loss is the difference between the sale price and the total cost to the store:

\[
\text{Operating Profit/Loss} = \text{Sale Price} - \text{Total Cost to Store} = 40.48 - 44.43 = -3.95
\]

### Conclusion:
The store incurred an **operating loss** of **$3.95** on the sale of the wine set.

Would you like more details or have any questions? 

Here are some related questions to expand on this topic:

1. How does markdown percentage affect overall profitability?
2. What would the operating profit/loss be with a different markdown percentage?
3. How would a change in overhead expenses impact the total cost to the store?
4. How can a business decide the ideal markdown percentage during clearance sales?
5. What pricing strategies can help a store minimize losses during markdowns?

**Tip:** When analyzing business profit and loss, consider both direct costs and indirect overheads to get a full picture of operating profitability.

A department store paid $37.52 for a wine set. Overhead expense is 14% of the regular selling price and profit is 10% of the regular selling price. During a clearance sale, the set was sold at a markdown of 18%. What was the operating profit or loss on the sale?

Learn how to calculate the operating profit or loss for a wine set sold during a clearance sale. The problem involves determining the regular selling price, overhead expenses, profit, and markdown percentage. Perfect for students in Grades 9-12 interested in practical applications of algebra and percentage calculations.

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