Problem 80 - Elementary Algebra

Question

A bookstore bought a used book from a student for \(\$ 20\). It then resold the book as a used book for \(\$ 85\). Find the percent markup.

Step-by-Step Solution

Answer

The percent markup is 325\%.

Step 1: Identify the Cost Price (CP)

The bookstore bought the book for \( \$20 \). This is the cost price (CP).

Step 2: Identify the Selling Price (SP)

The bookstore resold the book for \( \$85 \). This is the selling price (SP).

Step 3: Calculate the Markup Amount

The markup amount is the difference between the selling price and the cost price. \[ Markup = SP - CP = \$85 - \$20 = \$65 \]

Step 4: Calculate the Percent Markup

To find the percent markup, divide the markup amount by the cost price and multiply by 100. \[ \text{Percent Markup} = \left( \frac{\$65}{\$20} \right) \times 100 = 325\% \]

Key Concepts

Cost Price

The cost price, often abbreviated as CP, is the original amount paid to purchase an item. It is the starting point for understanding the financial aspects of any transaction. In our exercise, the bookstore bought a used book for \( \$20 \), making \( \$20 \) the cost price. Knowing this helps us identify how much was initially spent and sets the stage for further calculations related to selling and profit.
Remember the cost price is what you pay to acquire the product. In business, maintaining a clear record of the cost price is crucial for setting the right selling price and ensuring profitability.

Selling Price

The selling price, abbreviated as SP, is the price at which an item is sold to customers. It is essential in determining the revenue earned from sales. In our example, the bookstore resold the book for \( \$85 \).
To summarize:

• The initial amount paid for the book: \( \$20 \) (Cost Price)
• The amount received when the book is sold: \( \$85 \) (Selling Price)

The selling price must cover the cost price to avoid a loss and ideally should be higher to make a profit.

Markup Amount

The markup amount is the difference between the selling price and the cost price. It measures how much extra has been added to the cost price to arrive at the selling price. In our case, the markup amount is calculated as:
\[ Markup = SP - CP = \$85 - \$20 = \$65 \]
This \( \$65 \) represents the extra amount (or markup) the bookstore adds over the cost price to make a profit.
This concept is vital because it helps businesses understand their revenue streams and set the right prices to cover costs and achieve desired profit margins.

Percent Markup

Percent markup, or markup percentage, helps you understand the markup relative to the cost price in percentage terms. It is found by dividing the markup amount by the cost price and multiplying by 100. In this exercise, the percent markup is calculated as:
\[ \text{Percent Markup} = \left( \frac{\$65}{\$20} \right) \times 100 = 325\% \]
This means the selling price of the book is marked up by 325% over its cost price.
Understanding percent markup is critical in pricing strategies, ensuring the markup is sufficient to cover costs while being competitive in the market.