Calculating Commission Earnings for an Employee

When assessing the earning potential of an employee who is paid by commission, it is important to understand the relationship between their sales and their pay. In this scenario, we have an employee working 35 hours per week and we need to determine the dollar value of weekly sales, x, that the employee must achieve to earn more than $400 per week. However, for a precise inequality to be formulated, crucial information such as the commission rate is needed. In this article, we will outline the steps and provide a general framework for calculating commission-based earnings.

Understanding Commission Earnings

An employee is paid by commission when their earnings are directly tied to the sales they make. A typical commission structure is expressed as a percentage of the total sales. For example, an employee might earn a 5% commission on all sales they make. To calculate the commission earnings, the formula is:

E x times; c

E is the total earnings from commission. x is the total dollar value of sales. c is the commission rate expressed as a decimal.

Formulating the Inequality

Given that the employee needs to earn more than $400 per week, we can set up an inequality to find the minimum dollar value of weekly sales needed. Let's denote the commission rate as c. The inequality can be written as:

x times; c > 400

Where:

x is the minimum dollar value of sales. c is the commission rate, which must be specified.

Example Calculation

Suppose we know the commission rate is 5%, or 0.05 in decimal form. The inequality becomes:

x times; 0.05 > 400

To solve for x, divide both sides by 0.05:

x > 400 / 0.05

x > 8000

This means the employee must make at least $8000 in sales to earn more than $400 in commission.

Conclusion

Determining the dollar value of weekly sales needed for an employee to earn more than a certain amount involves understanding the commission structure. Without knowing the commission rate, it is impossible to set up a precise inequality. Once the commission rate is known, the inequality can be calculated and used to determine the minimum sales needed. This understanding is crucial for both employees and employers to manage expectations and profitability.