Calculating Selling Price, Sale Price, and Profit/Loss: A Retail Math Problem

Calculating Selling Price, Sale Price, and Profit/Loss for a Discounted Microwave

This example breaks down how to solve a common retail math problem involving calculating the regular selling price, sale price, and operating profit or loss. Let's dive in:

Problem: A retail store paid $44 for a microwave oven. Expenses are 27% of the regular selling price, and the required profit is 18% of the regular selling price. During an inventory sale, the microwave was marked down 40%.

(a) What was the regular selling price? (b) What was the sale price? (c) What was the operating profit or loss?

Solution:

(a) Finding the Regular Selling Price

1. Calculate Expenses: Expenses are 27% of the regular selling price (let's call this 'RSP'):

   • Expenses = 0.27 * RSP

2. Calculate Required Profit: The required profit is 18% of the RSP:

   • Required Profit = 0.18 * RSP

3. Set Up the Equation: The RSP is the sum of the cost price, expenses, and required profit:

   • RSP = Cost Price + Expenses + Required Profit
   • RSP = $44 + 0.27 * RSP + 0.18 * RSP

4. Solve for RSP:

   • RSP = $44 / (1 - 0.27 - 0.18)
   • RSP = $44 / 0.55
   • RSP = $80

   Therefore, the regular selling price of the microwave oven is $80.

(b) Finding the Sale Price

1. Apply the Markdown: The microwave was marked down 40% during the sale:

   • Sale Price = RSP - (Markdown * RSP)
   • Sale Price = $80 - (0.40 * $80)
   • Sale Price = $80 - $32
   • Sale Price = $48

   Therefore, the sale price of the microwave oven is $48.

(c) Calculating the Operating Profit or Loss

1. Calculate Total Cost:

   • Total Cost = Cost Price + Expenses
   • Total Cost = $44 + (0.27 * $80)
   • Total Cost = $44 + $21.60
   • Total Cost = $65.60

2. Calculate Operating Profit/Loss:

   • Operating Profit/Loss = Sale Price - Total Cost
   • Operating Profit/Loss = $48 - $65.60
   • Operating Profit/Loss = -$17.60

   Therefore, the operating loss is -$17.60. The store lost money on this sale.

Key Takeaways:

• Understanding how to calculate selling prices, sale prices, and profit/loss is crucial for retail businesses.
• This example highlights the importance of considering expenses and desired profit margins when pricing products.
• By breaking down the problem step-by-step, we can clearly see how each component contributes to the final result.