Chapter 10: Problem 20
One used-car salesperson receives a commission of
Short Answer
Step by step solution
Define Variables
Calculate the First Salesperson's Commission
Calculate the Second Salesperson's Commission
Set the Commissions Equal to Each Other
Solve for P
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Commission Calculations
The first salesperson receives a fixed amount plus a variable percentage of the sale price. Specifically, they earn a commission of
The second salesperson has a simpler structure; they earn a straight 6 percent of the final sale price. This means that their entire commission is directly tied to the sale price without any additional fixed component.
Recognizing these different structures is the first step in setting up the equation correctly to solve the problem.
Equation Solving
First, define the variable representing the unknown quantity: the final sale price of the car
For the first salesperson, the commission equation is:
From here, distribute and combine like terms to isolate
Percentage Operations
In our problem, the first salesperson earns a percentage of
The second salesperson earns 6% of the sale price directly:
These operations are essential for setting up the equations correctly. For instance, you need to understand how to calculate
GMAT Quantitative Section
The GMAT quantitative section has two main types of questions: problem-solving and data sufficiency. Problem-solving, like the provided exercise, requires applying math skills to find solutions.
Success in these questions depends on several factors:
- Understanding the problem.
- Defining variables.
- Writing equations.
- Performing accurate calculations.
The provided problem is an excellent example requiring no advanced mathematics but solid knowledge and application of basic arithmetic, percentages, and algebra.
Getting familiar with such problems prepares you for the range of questions you might encounter on the actual exam, helping you develop a strategy for approaching and solving them efficiently.