A Salesperson Is Paid A Base Salary Of $$300$ A Week Plus A $5%$ Commission On The Sales He Generates. Which Inequality Best Represents $s$$, The Amount Of Sales In Dollars He Must Generate To Earn More Than
Introduction
In the world of sales, a salesperson's earnings are often a combination of a base salary and a commission on the sales they generate. In this scenario, we have a salesperson who earns a base salary of $300 per week, plus a 5% commission on the sales they generate. The question is, how much in sales must they generate to earn more than a certain amount? In this article, we will explore the inequality that best represents the amount of sales in dollars the salesperson must generate to earn more than a certain amount.
Understanding the Commission Structure
Let's break down the commission structure for the salesperson. They earn a base salary of $300 per week, which is a fixed amount. In addition to this, they earn a 5% commission on the sales they generate. This means that for every dollar they sell, they earn an additional 5 cents. To calculate the total earnings, we need to add the base salary and the commission earned from sales.
Calculating Total Earnings
Let's say the salesperson generates x dollars in sales. Their total earnings would be the base salary plus the commission earned from sales. The commission earned from sales is 5% of the sales generated, which is 0.05x. Therefore, the total earnings can be represented as:
Total Earnings = Base Salary + Commission = 300 + 0.05x
Representing the Inequality
The question asks which inequality best represents the amount of sales in dollars the salesperson must generate to earn more than a certain amount. Let's say the certain amount is y. We want to find the amount of sales in dollars the salesperson must generate to earn more than y. This can be represented as:
300 + 0.05x > y
Simplifying the Inequality
To simplify the inequality, we can subtract 300 from both sides:
0.05x > y - 300
Dividing by 0.05
To isolate x, we can divide both sides by 0.05:
x > (y - 300) / 0.05
Simplifying the Right-Hand Side
To simplify the right-hand side, we can multiply the numerator and denominator by 100:
x > (100y - 30000) / 5
x > 20y - 6000
Conclusion
In conclusion, the inequality that best represents the amount of sales in dollars the salesperson must generate to earn more than a certain amount is:
x > 20y - 6000
This inequality takes into account the base salary and the commission structure, and provides a clear representation of the amount of sales in dollars the salesperson must generate to earn more than a certain amount.
Example Use Case
Let's say the salesperson wants to earn more than $1000 per week. We can plug in y = 1000 into the inequality:
x > 20(1000) - 6000 x > 20000 - 6000 x > 14000
This means that the salesperson must generate at least $14,000 in sales to earn more than $1000 per week.
Conclusion
Introduction
In our previous article, we explored the inequality that best represents the amount of sales in dollars a salesperson must generate to earn more than a certain amount. We broke down the commission structure, calculated the total earnings, and simplified the inequality to provide a clear representation of the amount of sales in dollars the salesperson must generate to earn more than a certain amount. In this article, we will answer some frequently asked questions related to the salesperson's commission inequality.
Q: What is the base salary of the salesperson?
A: The base salary of the salesperson is $300 per week.
Q: What is the commission rate of the salesperson?
A: The commission rate of the salesperson is 5% of the sales generated.
Q: How is the total earnings calculated?
A: The total earnings are calculated by adding the base salary and the commission earned from sales. The commission earned from sales is 5% of the sales generated, which is 0.05x.
Q: What is the inequality that represents the amount of sales in dollars the salesperson must generate to earn more than a certain amount?
A: The inequality that represents the amount of sales in dollars the salesperson must generate to earn more than a certain amount is:
x > 20y - 6000
Q: How do I use the inequality to determine the amount of sales in dollars the salesperson must generate to earn more than a certain amount?
A: To use the inequality, you need to plug in the certain amount (y) into the inequality and solve for x. For example, if the salesperson wants to earn more than $1000 per week, you would plug in y = 1000 into the inequality:
x > 20(1000) - 6000 x > 20000 - 6000 x > 14000
This means that the salesperson must generate at least $14,000 in sales to earn more than $1000 per week.
Q: What if the salesperson wants to earn more than a certain amount per month? How do I adjust the inequality?
A: If the salesperson wants to earn more than a certain amount per month, you need to adjust the inequality to account for the number of weeks in a month. For example, if the salesperson wants to earn more than $4000 per month, you would multiply the certain amount by 4 (since there are approximately 4 weeks in a month):
x > 20(4000) - 6000 x > 80000 - 6000 x > 74000
This means that the salesperson must generate at least $74,000 in sales to earn more than $4000 per month.
Q: What if the salesperson wants to earn more than a certain amount per year? How do I adjust the inequality?
A: If the salesperson wants to earn more than a certain amount per year, you need to adjust the inequality to account for the number of weeks in a year. For example, if the salesperson wants to earn more than $50,000 per year, you would multiply the certain amount by 52 (since there are approximately 52 weeks in a year):
x > 20(50000) - 6000 x > 1000000 - 6000 x > 999000
This means that the salesperson must generate at least $999,000 in sales to earn more than $50,000 per year.
Conclusion
In this article, we answered some frequently asked questions related to the salesperson's commission inequality. We provided examples of how to use the inequality to determine the amount of sales in dollars the salesperson must generate to earn more than a certain amount, and how to adjust the inequality to account for different time periods.