Problem 57 - Algebra for College Students

Question

A real-estate agent earned \(\$ 6300\) commission on a property sale of \(\$ 210,000 .\) What is her rate of commission?

Step-by-Step Solution

Answer

3%

Step 1: Understand the Values

Identify the total commission earned (\(6300) and the total property sale price (\)210,000).

Step 2: Define the Commission Rate Formula

Use the formula for commission rate, which is \[ \text{Commission Rate} = \frac{\text{Commission Earned}}{\text{Total Sale Price}} \times 100 \text{}\].

Step 3: Substitute the Values

Plug the values into the formula: \[ \text{Commission Rate} = \frac{6300}{210000} \times 100\].

Step 4: Perform the Calculation

Calculate the result: \[ \text{Commission Rate} = \frac{6300}{210000} \times 100 = 3\text{\boldmath %}\].

Key Concepts

Real Estate Transactions

In the world of real estate, transactions can often be complex. However, understanding the financial aspects is crucial. One key financial aspect is the commission that agents earn when a property is sold. A real estate transaction typically involves the following steps:

• Listing the Property: An agent helps the seller to list the property on the market.
• Marketing: The agent markets the property to attract potential buyers.
• Negotiation: The agent assists in negotiating the terms of the sale between the buyer and seller.
• Closing: Once an agreement is reached, the deal is closed, and the agent earns a commission.

The commission is usually a percentage of the property’s sale price. This makes it essential for agents to understand how to calculate their commission rate efficiently.

Percentage Calculations

Percentage calculations are crucial for many real-world applications, including calculating commissions in real estate transactions. A percentage represents a part of the whole and is often used to express proportions. The basic formula for calculating a percentage is:
\(\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\) In our example, the 'part' is the commission earned (\text{\boldmath \(6300\boldmath }) and the 'whole' is the total sale price of the property (\text{\boldmath \)210,000\boldmath }). By substituting these values into the formula, you can calculate the commission rate:
\( \text{Commission Rate} = \frac{6300}{210000} \times 100 = 3\text{%}\) Breaking down calculations into these steps helps simplify complex problems.

Basic Algebra

Basic algebra often forms the foundation for many calculations, including those involving percentages. Algebra provides tools to solve equations and manipulate variables to find desired values. When working with algebra:

• Identify the variables you are working with.
• Understand the relationships between these variables.
• Use the appropriate formulas to solve for the unknowns.

In the context of our commission calculation, we have the formula:
\(\text{Commission Rate} = \frac{\text{Commission Earned}}{\text{Total Sale Price}} \times 100\) By recognizing the commission earned as one variable and the total sale price as another, you can set up the equation and solve for the commission rate. The step-by-step approach helps in understanding how each component fits into the larger equation.