
Question content area top

Part 1

A department store paid 

​$37.5237.52 

for 

a wine seta wine set. 

Overhead expense is 

14 %14% 

of the regular selling price and profit is 

10 %10% 

of the regular selling price. During a clearance​ sale, the set was sold at a markdown of 

18 %.18%. 

What was the operating profit or loss on the​ sale?

To determine the operating profit or loss on the sale of the wine set, we need to break down the cost, selling price, and profit margin components.

### Step 1: Define variables and relationships
- Let the **regular selling price** of the wine set be $ S $.
- The **overhead expense** is 14% of the regular selling price:  
  $ \text{Overhead expense} = 0.14S $.
- The **profit margin** is 10% of the regular selling price:  
  $ \text{Profit} = 0.10S $.
- The **cost price** (which is what the store paid for the set) is $37.52.

During the clearance sale, the set was sold at a markdown of 18%. So, the **sale price** becomes:  
$ \text{Sale price} = (1 - 0.18) \times S = 0.82S $.

### Step 2: Calculate the operating profit or loss
The operating profit or loss is calculated by subtracting the total expenses (cost + overhead) from the sale price. Let's calculate this step-by-step.

1. **Sale price** = $ 0.82S $.
2. **Cost price** = $37.52.
3. **Overhead expense** = $ 0.14S $.

Operating profit or loss is:

\[
\text{Operating Profit/Loss} = \text{Sale price} - \text{Cost price} - \text{Overhead expense}
\]
\[
= 0.82S - 37.52 - 0.14S
\]
\[
= 0.68S - 37.52
\]

### Step 3: Find the regular selling price $ S $
We know that the **profit** is 10% of the regular selling price, so:

\[
\text{Profit} = 0.10S
\]

Now, the total expenses (cost + overhead) should equal the revenue minus the profit:

\[
37.52 + 0.14S = 0.82S - 0.10S
\]

Let me solve for $ S $.The regular selling price of the wine set is approximately **$64.69**.

### Step 4: Calculate the operating profit or loss
Now that we know the regular selling price, we can calculate the operating profit or loss:

\[
\text{Operating Profit/Loss} = 0.68 \times 64.69 - 37.52
\]

Let me calculate this.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can guide you through solving the problem step-by-step manually. Let me know if you'd like to proceed that way!

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 when a wine set is sold at a markdown. The problem involves overhead expenses of 14%, profit of 10%, and an 18% markdown on the regular selling price. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation