Problem 49 - Elementary Algebra

Question

A retailer buys an item for \(\$ 40\), resells it for \(\$ 50\), and claims that she is making only a \(20 \%\) frofit. Is her claim comect?

Step-by-Step Solution

Answer

No, her claim is incorrect; the profit is 25%, not 20%.

Step 1: Calculate the Profit Amount

The profit amount is the difference between the selling price and the buying price. So, the profit amount is calculated as follows: \[\text{Profit} = \text{Selling Price} - \text{Cost Price} = 50 - 40 = 10 \]

Step 2: Calculate the Profit Percentage

The profit percentage is computed by dividing the profit amount by the cost price and then multiplying by 100. This is expressed as: \[\text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 = \left( \frac{10}{40} \right) \times 100 = 25\%\]

Step 3: Compare the Calculated Profit Percentage with the Claimed Percentage

The retailer claims a profit of \(20\%\). However, we calculated a profit percentage of \(25\%\). Thus, her claim is incorrect because the actual profit percentage is higher than what she claimed.

Key Concepts

Understanding Percentage

Percentage is a fundamental concept used to compare and express quantities relative to each other. When we talk about percentages, we are discussing a fraction out of 100. This makes it an incredibly useful tool in expressing parts of a whole.

In calculating profits, percentages help understand how much profit is made compared to the initial costs. For example, if you have a profit percentage of 25%, it means for every dollar spent, 25 cents is earned as profit.

• To find the percentage of any number, divide the part by the whole and multiply by 100.
• This method is particularly useful in financial calculations, allowing for easy comparison between different investments or sales.

Understanding percentage not only simplifies the representation of differences but also provides insight into profitability, growth, and efficiency in both personal and business finances.

Decoding Cost Price

The cost price represents the original price paid to acquire a product. It is an essential factor in determining how much profit you make from selling an item.

In the context of profit calculation, it's vital to know the cost price because it serves as the baseline for comparing profits against selling prices.

• The cost price includes any expenses directly associated with acquiring the goods such as purchase costs.
• Understanding the cost price allows businesses to set selling prices that ensure profitability.

To effectively manage finances, knowing the exact cost price is critical, as it affects pricing decisions and overall financial planning.

Exploring Selling Price

The selling price is the amount at which a product is sold to customers. It incorporates the cost price while also aiming to include a profit margin.

Determining the correct selling price is crucial for ensuring that a business remains profitable. It reflects not just the cost, but also market trends, customer demand, and competitor pricing.

• The selling price should cover the cost price plus any desired profit margin to achieve financial goals.
• Businesses might adjust the selling price based on various factors, including demand and economic conditions.
• An ideally set selling price aims not only to maximize profits but also to remain attractive to consumers.

A well-chosen selling price can help maintain competitiveness and sustainability in a business environment.