Math Problem Statement
A store purchases camcorders for $500 each. Its overhead expenses are 15% of the cost and it wants an operating profit of $250 on the sale of each camcorder. The store cannot sell their camcorders at regular selling price and markdown the price by $100. Calculate the rate of markdown and the reduced selling price.
Solution
Let's break this problem down step by step to calculate the rate of markdown and the reduced selling price.
Step 1: Calculate Overhead Expenses
The store incurs overhead expenses that are 15% of the cost price of each camcorder.
- Cost price of the camcorder = $500
- Overhead expenses = 15% of $500
So, the total overhead expenses are $75.
Step 2: Calculate the Target Selling Price
The store wants to make an operating profit of $250 on each camcorder. The target selling price will be the sum of the cost price, overhead expenses, and desired profit.
- Cost price = $500
- Overhead expenses = $75
- Desired profit = $250
So, the regular selling price is $825.
Step 3: Calculate the Reduced Selling Price
The store marks down the camcorder by $100, so the reduced selling price is:
Step 4: Calculate the Rate of Markdown
The rate of markdown is the percentage by which the price was reduced compared to the regular selling price.
Here, the markdown amount is $100 and the original selling price is $825.
Final Answer:
- The rate of markdown is approximately 12.12%.
- The reduced selling price is $725.
Would you like more details or have any questions?
Here are some related questions you might find interesting:
- What would happen to the markdown rate if the store marked down the price by $150 instead of $100?
- How much profit would the store make if it sold the camcorder at the reduced price of $725?
- What would the rate of markdown be if the store increased overhead expenses to 20%?
- If the cost price of the camcorder changed to $600, how would that affect the selling price and markdown rate?
- What is the minimum price the store could sell the camcorder at and still cover its overhead and desired profit?
Tip: When calculating markdown percentages, always remember to divide the markdown amount by the original price, not the new price.
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Math Problem Analysis
Mathematical Concepts
Percentages
Cost and Profit Calculation
Markdown Rate Calculation
Formulas
Overhead expenses = Cost price * Overhead percentage
Target Selling Price = Cost price + Overhead expenses + Desired profit
Rate of Markdown = (Markdown amount / Original selling price) * 100
Theorems
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Suitable Grade Level
Grades 8-10
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