Problem 48 - Algebra for College Students

Question

Solve each percent problem. David sold his house for \(\$ 159,000\). He got this amount knowing that he would have to pay a \(6 \%\) commission to his agent. What amount did he have after the agent was paid?

Step-by-Step Solution

Answer

David has \(\$ 149,460\) after the agent was paid.

Step 1 - Understand the Problem

David sold his house for \(\$ 159,000\) and needs to pay a \(6\%\) commission to his agent. The goal is to find out the amount David has left after the commission is paid.

Step 2 - Calculate the Commission Amount

To find the commission amount, multiply the total selling price by the commission rate: \(\text{Commission} = 159,000 \times \frac{6}{100} = 159,000 \times 0.06 = \$ 9,540\).

Step 3 - Subtract the Commission from the Selling Price

Subtract the commission amount from the total selling price to find out how much David has left: \(159,000 - 9,540 = \$ 149,460\).

Step 4 - Verify the Calculation

Double-check the calculations to ensure accuracy: \(159,000 \times 0.06 = 9,540\) and \(159,000 - 9,540 = 149,460\). Therefore, David has \(\$ 149,460\) left after paying the commission.

Key Concepts

Percent Calculation

Understanding percent calculation is essential in many real-world scenarios. A percent is a way of expressing a number as a fraction of 100. For instance, a 6% commission means 6 out of 100 parts of the total amount. To calculate a percentage of a given number:

• First, convert the percent to a decimal by dividing by 100, which turns 6% into 0.06.
• Next, multiply the decimal by the total amount. For the exercise, we calculated 6% of \$159,000 by performing the calculation \(159,000 \times 0.06 = 9,540\).

Knowing how to compute percentages helps to manage finances, discounts, and various other applications effectively.

Commission Calculation

A commission is a fee paid to an agent or broker for their services, typically calculated as a percent of the total transaction. To determine the commission:

• First, identify the percent rate of the commission (in this case, 6%).
• Next, convert this percent to a decimal (6% becomes 0.06).
• Then, multiply the selling price by the decimal to find the commission amount. For David's house sale at \$159,000 and a 6% commission, we get \(159,000 \times 0.06 = 9,540\).

This amount, \$9,540, is the fee paid to the agent. Subtract the commission from the total selling price to determine David's remaining amount. Therefore, \(159,000 - 9,540 = 149,460\). After paying the commission, David has \$149,460 left.

Real Estate Math

In real estate, math is critical for various transactions, including buying, selling, and investing in properties. Here, understanding percent calculations and commissions is crucial. Selling a house often involves paying a real estate agent a commission fee, calculated as a percentage of the selling price. Let’s break it down using David's example:

• David sold his house for \$159,000.
• His agent's commission was 6%, equating to \$9,540 (calculated as \(159,000 \times 0.06\)).
• After subtracting the commission, David has \$149,460 remaining.

Real estate math ensures that transactions are transparent and both parties understand the financial aspects involved, making it a fundamental skill for anyone involved in property dealings.