Problem 41 - Elementary Algebra Within Reach

Question

Commission A real estate agency receives a commission of \(\$ 14,506.50\) for the sale of a \(\$ 152,700\) house. What percent commission is this?

Step-by-Step Solution

Answer

The real estate agency's commission is approximately 9.5% of the house's total value.

Step 1: Determine the Initial Values

The given information from the exercise is: commission amount of \$14,506.50 and the total value of house which is \$152,700.

Step 2: Formulate the Percentage Formula

The formula to calculate the percentage is: Percentage = (Part/Whole) * 100.

Step 3: Apply the Percentage Formula

In our case, the 'Part' is the commission amount and the 'Whole' is the value of the house. Substitute these values into the formula. This gives: Percentage = (\$14,506.50/\$152,700) * 100.

Step 4: Calculate the Percentage

After substituting the values, solve the equation to find out the commission percentage.

Key Concepts

Understanding the Real Estate Market

The real estate market is an economic sector that involves the buying, selling, and renting of land and properties. It's significant to understand how this market functions because it impacts various facets of everyday life, from housing to investments. Real estate transactions often involve complex processes and terms.
When buying or selling properties, factors such as location, market trends, and property conditions play into the price. Real estate agents are professionals who help people navigate these transactions, ensuring that both parties reach a fair agreement.
- **Key elements of the real estate market include:** - **Supply and Demand:** High demand with low supply can increase prices. - **Location:** Some areas are more desirable, affecting property values. - **Market Trends:** Seasonal fluctuations or economic changes influence market activity. Understanding these components can help you make informed decisions whether buying, selling, or investing in real estate.

Decoding Commission Calculation

In the real estate world, commission calculation is a central concept, especially for real estate agents. A commission is a sum paid to an agent for their services in facilitating a sale. It's usually a percentage of the property's selling price.
Calculating this percentage helps determine how much an agent earns from each sale. To calculate, the commission amount is divided by the total sale price and then multiplied by 100. This way, you get the percentage of the sale that constitutes the commission.

• Commission Amount: The fixed sum earned from a sale.
• Total Sale Price: The complete selling price of the property.
• Formula: Commission Percentage = (Commission Amount / Total Sale Price) x 100

This calculation is crucial for understanding how much of the property's price goes towards paying the agent and can vary widely depending on the market and agency.

Applying Mathematical Formulas

Mathematical formulas help simplify complex calculations, breaking them down into manageable steps. In real estate and other fields, these formulas allow professionals to conduct precise calculations.
**Understanding the Percentage Formula**:
The percentage formula is straightforward but powerful: \[\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\]In this formula:- **Part** represents the portion or segment you are analyzing, such as a commission or tax.- **Whole** is the total amount, like the sale price of a house.
Armed with this simple formula, anyone can quickly find out what fraction of a total is represented by a specific part. This is particularly useful for financial transactions in the real estate market, enabling all parties to have clear, quantifiable information for decision-making.