Question

Wages of a Car Salesperson Dan receives 525 dollar per week for selling new and used cars. He also receives \(5 \%\) of the profit on any sales. Write a linear equation that represents Dan's weekly salary \(S\) when he has sales that generate a profit of \(x\) dollars.

Short answer

\(S = 525 + 0.05x\)

Step-by-step solution

- Identify the fixed component of the salary

Dan receives a fixed weekly salary of 525 dollars regardless of his sales. This forms the constant part of the linear equation.

- Determine the variable component of the salary

Dan also earns 5% of the profit generated from his sales. This can be mathematically represented as 0.05 times the profit, where the profit is denoted by \(x\).

- Combine the fixed and variable components

Combine the fixed salary and the percentage of profit to form the linear equation. The total weekly salary \(S\) is given by the sum of the fixed salary and the variable profit component. Therefore, the equation becomes \(S = 525 + 0.05x\).

Key concepts

salary calculation

Calculate the weekly salary of a car salesperson involves two parts.
Dan, our example salesperson, has a fixed weekly payment of 525 dollars. This amount does not change no matter how many cars he sells or the profit he generates from those sales.
The fixed portion brings stability and a guaranteed income each week. Another component of his wage is the variable part, which depends on his sales performance. He earns 5% of the profit generated from his sales.
To represent the variable component mathematically, we can use 0.05 times the profit, where the profit is denoted by \( x \).
By combining both the fixed salary and the percentage of the profit, we get Dan's total weekly salary. The linear equation representing this combination is \( S = 525 + 0.05x \).
This linear equation helps to calculate Dan's weekly earnings based on the profit he generates from car sales.

profit percentage

Understanding profit percentage is crucial for comprehending the variable component of Dan's salary.
The profit percentage indicates a part of the profit earned on top of the costs. For Dan, the percentage is 5%.
To find Dan's additional earnings from sales, we calculate 5% or 0.05 of the total profit. For instance, if Dan generates a profit of 1000 dollars, his additional earning will be 0.05 multiplied by 1000, which gives him 50 dollars.
Combining this amount with his fixed salary of 525 dollars gives his total salary for that week.
This practice is common in sales jobs to incentivize employees. Additional earnings from the profit component keep salespersons motivated and reward their performance.
Therefore, the profit percentage plays a significant role in sales-related jobs, directly impacting the variable income component.

fixed and variable components

In many jobs, including sales positions like Dan’s, salaries include fixed and variable components.
The fixed component ensures a stable income. It is a constant amount that an employee receives regularly, regardless of the company’s performance or the employee’s personal achievements. For Dan, this is fixed at 525 dollars per week.
The variable component fluctuates based on performance. It provides an incentive for employees to perform better and achieve more, as their salary can increase with better performance. Dan’s variable component is 5% of the profit he generates.
Such a structure encourages employees to work harder, aiming to increase their sales and, in turn, their total earnings. Combining both fixed and variable components, an employee's total salary can be represented using a linear equation. For Dan, this is reflected in \( S = 525 + 0.05x \), where \( S \) is his total salary and \( x \) is the profit made from sales.
Understanding fixed and variable salary components helps employees grasp how their earnings are structured and motivates them to maximize their performance for better rewards.