Problem 55 - College Algebra and Calculus: An Applied Approach

Question

Wholesale Price A store marks up a power drill \(60 \%\) from its wholesale price. In a clearance sale, the price is discounted by \(25 \%\). The sale price is \(\$ 21.60\). What was the wholesale price of the power drill?

Step-by-Step Solution

Answer

The wholesale price of the power drill was \$18.

Step 1: Define and understand the problem

The power drill's sale price is given as $21.60. This is after it was marked up by 60% and then discounted by 25%. We need to work backwards to find the original wholesale price. Let's label the initial wholesale price as \(W\).

Step 2: Find the price before the clearance sale

If a 25% discount results in a sale price of $21.60, then before discount the price was (\(21.60 ÷ (1 - 0.25)\)) which results in $28.80. The markdown formula is sale price = original price * (1 - discount rate).

Step 3: Find the original wholesale price

The markup formula is selling price = cost * (1 + markup percent). So, the wholesale price \(W\) would be \( 28.80 ÷ (1 + 0.60) \). This would give us the wholesale price as \$18.

Key Concepts

Markup and Discount Calculations

Understanding markup and discount calculations is essential when analyzing sales deals and pricing strategies. Markup refers to the percentage added to the cost price to determine the selling price, while a discount is a reduction offered from that selling price.
In our given problem, the power drill initially had a wholesale price, from which a 60% markup was applied. Markup can be calculated using the formula:
- Selling Price = Cost Price × (1 + Markup Percentage)
After the markup, a 25% discount was offered during a clearance sale. Discount impacts the selling price by reducing it. The formula for discount calculation is:
- Sale Price = Original Price × (1 - Discount Rate)
It is essential to work through these formulas step-by-step to decipher the original price from a final sale price after applying these adjustments.

Wholesale Pricing

Wholesale pricing refers to the original cost of a product that retailers pay before any markups or added expenses. It's crucial for retailers as it impacts the profit margins when selling to customers.
Typically, stores determine the retail price by applying a certain markup on the wholesale price. The goal is to cover costs and potentially earn profits. Here, the power drill was first bought at its wholesale price, which was later marked up by 60% before it was sold to consumers.
Understanding wholesale pricing helps in determining how much more a consumer pays compared to the initial cost incurred by the retailer. Imagine knowing that your wholesale price is such that, even after a markup and a later discount during a sale, you still make a fair profit. That's why retailers always calculate these values judiciously to make sure they're competitive while also strategic.

Step-by-Step Solutions

Breaking down problems into manageable steps is key to understanding and solving complex algebra problems effectively. This method encourages a logical approach by clearly defining each step, like peeling layers of an onion.
In the drill pricing problem, the first step was to acknowledge the sale price ($21.60) following the clearance discount. The next step traced back to find the pre-discount price of $28.80, using the formula: pre-discount price = sale price ÷ (1 - Discount Rate).
Finally, to discover the original wholesale price, the problem reversed the markup calculation using: wholesale price = selling price ÷ (1 + Markup Percentage). This logical sequence ensures that each mathematical adjustment is properly accounted for, helping to clarify complex pricing and adjustments in real-world contexts.