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Chapter 2: Problem 77

The annual base salary for a sales position is \(\$ 45,000\). An additional \(12.5 \%\) commission is earned on any sales over \(\$ 750,000\). Find the amount of additional sales needed for the total annual salary to be \(\$ 90,000\).

Short Answer

Expert verified
$360,000 in additional sales is needed.

Step by step solution

01

Identify the Base Salary and Commission Requirement

The annual base salary is \( \$ 45,000 \). The total annual salary goal is \( \$ 90,000 \). The commission rate is \( 12.5 \% \) on sales over \( \$ 750,000 \).
02

Set Up the Equation

Let \( x \) represent the additional sales needed over \( \$ 750,000 \). The commission earned on these additional sales would be \( 0.125x \). The equation for the total salary is: \[ 45000 + 0.125x = 90000 \]
03

Solve for x

Isolate \( x \): \[ 45000 + 0.125x = 90000 \] Subtract \( 45000 \) from both sides: \[ 0.125x = 45000 \] Divide both sides by \( 0.125 \): \[ x = \frac{45000}{0.125} \] Calculate the result: \[ x = 360000 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Base Salary
In a sales job, the base salary is the guaranteed amount of salary a sales representative earns regardless of how much they sell. This provides financial stability throughout the year. For instance, in our exercise, the base salary is \( \$45,000 \). Understanding base salary is crucial because it forms the foundation of your earnings before adding commissions.
Commission Rate
The commission rate is the percentage of sales that a salesperson earns as a reward. This is usually applied to sales exceeding a certain threshold. In our example, the commission rate is \(12.5\%\). This means for every dollar sold over \(\$750,000\), the salesperson earns \(12.5\ cents\). Calculating commissions can be motivating because higher sales bring in more income.
Solving Linear Equations
Solving linear equations is a key mathematical skill when calculating commissions and understanding salary structures. Our equation, \(45000 + 0.125x = 90000\), helps us find out how much additional sales are needed. Here鈥檚 a short breakdown:
-First, isolate \(x\) by subtracting \(45000\) from both sides, yielding \(0.125x = 45000\).
-Then, divide both sides by \(0.125\) to find \(x\). Successfully solving such equations helps in making informed financial decisions.
Additional Sales
Additional sales refer to the total sales beyond a pre-set threshold required before commission is earned. In this case, sales above \(\$750,000\) are considered additional sales. Using the solved equation, we determined that \(\$360,000\) in additional sales is needed to reach the target salary of \(\$90,000\). Knowing this can help salespersons set realistic and achievable sales goals.

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Most popular questions from this chapter

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