Problem 40 - Algebra for College Students

Question

Solve each equation. A textbook costs a bookstore \(\$ 45\), and the store sells it for \(\$ 60\). Find the rate of profit based on the selling price.

Step-by-Step Solution

Answer

The rate of profit based on the selling price is 25%.

Step 1: Identify cost and selling price

The cost price of the textbook is given as $45, and the selling price is given as $60.

Step 2: Calculate profit

The profit is the difference between the selling price and the cost price. Calculate profit:\[ \text{Profit} = \text{Selling Price} - \text{Cost Price} = 60 - 45 = 15\]

Step 3: Calculate profit rate based on selling price

The profit rate based on the selling price is calculated by dividing the profit by the selling price and then multiplying by 100 to get a percentage:\[\text{Profit Rate} = \left( \frac{\text{Profit}}{\text{Selling Price}} \right) \times 100 = \left( \frac{15}{60} \right) \times 100\]

Step 4: Simplify profit rate

Simplify the expression to find the profit rate:\[\left( \frac{15}{60} \right) \times 100 = 0.25 \times 100 = 25\%\]

Key Concepts

Selling Price

The selling price of a product is the price at which it is sold to customers. In our example, the textbook is sold for $60. This is the amount the customer pays to purchase a single textbook.
The selling price is crucial for calculating profit, as it helps determine how much money is made after covering the initial cost. It can also give insights into setting competitive prices in the market.

• It is often higher than the cost price to ensure the business makes a profit.
• Factors influencing the selling price can include market trends, customer demand, and perceived value of the product.

Cost Price

The cost price is the amount the bookstore pays to acquire the textbook. In this exercise, the cost price is $45. This is how much it costs the store before any profit is added.
Understanding the cost price helps in knowing the minimum amount to cover the expenses. Selling below cost price can lead to a loss, which affects the sustainability of the business.

• Includes expenses like production costs, shipping, and handling fees.
• Often, the goal is to have a selling price higher than the cost price.

Profit Rate

The profit rate is a measure of how much profit is made relative to the selling price. This is expressed as a percentage, making it easier to compare profitability across different products or ventures.
In this case, the profit rate is calculated using the formula: \[ \text{Profit Rate} = \left( \frac{\text{Profit}}{\text{Selling Price}} \right) \times 100 \]
First, find the profit by subtracting the cost price from the selling price, which gives us $15. Then, the profit rate is calculated as:\[ \left( \frac{15}{60} \right) \times 100 = 25\% \]This means the bookstore makes a 25% profit on each textbook sold relative to its selling price.

• Helps businesses evaluate the effectiveness of their pricing strategies.
• Higher profit rates can indicate better pricing strategies or cost management.