Question

Translate to an equation and solve. Kera is a salesperson at a car dealership and earns \(25 \%\) of the profit in commission. If in one month the dealership made a profit of \(\$ 9680\) from her sales, how much will she receive as commission?

Short answer

Answer: Kera will receive a commission of $2420.

Step-by-step solution

Understand the given information

Kera earns 25% commission of the profit, and the profit made by the dealership in one month from her sales is $9680. Our task is to find out how much Kera will receive as commission.

Write the equation to find the commission

To find Kera's commission, we need to calculate 25% of the profit. We can write the equation: Commission = (25 / 100) * Profit

Substitute the profit value in the equation

Now, we will substitute the value of profit, which is $9680, in the equation: Commission = (25 / 100) * 9680

Calculate the commission

Next, we will solve the equation to find the commission Kera receives: Commission = (25 / 100) * 9680 = 0.25 * 9680 = 2420 So, Kera will receive a commission of $2420.

Key concepts

Percentage Calculation

Percentage calculations are an essential part of prealgebra that allow us to express a number as a fraction of 100. In this exercise, we need to find out how much commission Kera earns from the total profit made by the car dealership. The percentage given is 25%, which is Kera's commission rate.

To calculate 25% of a given amount, you multiply that amount by 0.25. Here's why:

• Percent literally means "per hundred," so 25% equals 25 out of every 100 units.
• To convert the percentage to a decimal, divide by 100: \(\frac{25}{100} = 0.25\).

This conversion is necessary because it's easier to work with decimals in multiplication than percentages. Using this method, we calculated Kera's commission as 25% of \(9680, resulting in \)2420.

Basic Algebra

Basic algebra involves forming equations to represent real-world situations and finding solutions to these equations. In this example, we need to determine how much Kera earns as a commission. The problem involves simple multiplication within an equation.

Here, the equation is:

• Commission = (25 / 100) * Profit
• By substituting the given value of profit: Commission = 0.25 * 9680

The solution involves applying basic algebraic principles by substituting known values into the equation and then simplifying. This approach is universally applicable to many different algebraic problems, making algebra a vital tool in problem-solving. The solution results in Kera receiving $2420.

Problem-Solving Steps

Solving a mathematical problem, especially in prealgebra, involves systematic steps that help clarify the problem and find a solution. Here’s the process we followed to solve Kera's commission problem:

• Understand the problem: Determine what is given, what is asked, and what mathematical operations will help solve the problem.
• Formulate the equation: Translate the problem into a mathematical equation using appropriate operators, like multiplication for percentage calculation.
• Substitute values: Insert the known values (here, the given profit amount) into the equation.
• Solve the equation: Perform the arithmetic operation to find the answer.

These steps demonstrate a clear and logical approach to problem-solving, helping to ensure accuracy and thorough understanding.