Calculating the Additional Income Required

Oct 13, 2025 by talynt.org 28 views

Understanding the Commission Structure

John works at a car dealership where he earns a fixed weekly income of $300, plus a commission equal to 2% of his total sales for the week. His goal is to earn at least $700 for the week. To determine the minimum amount of total sales John must have to reach his goal, we need to calculate the additional income he needs to earn through his commission.

Calculating the Additional Income Required

To calculate the additional income John needs to earn through his commission, we subtract his fixed weekly income from his goal:

$700 (goal) - $300 (fixed income) = $400 (additional income required)

Calculating the Minimum Sales Required

Since John earns a commission of 2% on his total sales, we can set up an equation to represent the situation:

Commission = 2% of Total Sales Commission = 0.02 x Total Sales

We know that the commission earned must be at least $400 to reach John's goal. Therefore, we can set up the following equation:

0.02 x Total Sales ≥ $400

To solve for the minimum total sales required, we can divide both sides of the equation by 0.02:

Total Sales ≥ $400 / 0.02 Total Sales ≥ $20,000

Conclusion

To reach his goal of earning at least $700 for the week, John must have a minimum of $20,000 in total sales. This is calculated by determining the additional income required through his commission and then dividing that amount by the commission rate of 2%.

Example Use Case

Suppose John sells 10 cars in a week, each with a sale price of $2,000. His total sales for the week would be:

10 cars x $2,000 per car = $20,000

In this scenario, John would meet his minimum sales requirement of $20,000 and would earn a commission of:

$20,000 x 0.02 = $400

Adding this commission to his fixed weekly income of $300, John would earn a total of:

$400 (commission) + $300 (fixed income) = $700

This example illustrates how John can meet his minimum sales requirement and earn his desired income through his commission.

Key Takeaways

John's goal is to earn at least $700 for the week.
He earns a fixed weekly income of $300, plus a commission of 2% on his total sales.
To reach his goal, John must have a minimum of $20,000 in total sales.
The commission earned must be at least $400 to meet John's goal.

Mathematical Formulation

Let's represent the situation mathematically:

Let x be the total sales required to reach John's goal. Let y be the commission earned. Let z be the fixed weekly income.

We know that:

y = 0.02x z = $300 x + y ≥ $700

Substituting the expression for y into the inequality, we get:

x + 0.02x ≥ $700 1.02x ≥ $700

Dividing both sides of the inequality by 1.02, we get:

x ≥ $700 / 1.02 x ≥ $20,000

Understanding the Commission Structure

Q&A Session

Q: What is the commission structure for John's job? A: John earns a fixed weekly income of $300, plus a commission equal to 2% of his total sales for the week.

Q: What is John's goal for the week? A: John's goal is to earn at least $700 for the week.

Q: How much additional income does John need to earn through his commission? A: To calculate the additional income John needs to earn through his commission, we subtract his fixed weekly income from his goal:

$700 (goal) - $300 (fixed income) = $400 (additional income required)

Q: How do we calculate the minimum sales required to reach John's goal? A: Since John earns a commission of 2% on his total sales, we can set up an equation to represent the situation:

Commission = 2% of Total Sales Commission = 0.02 x Total Sales

We know that the commission earned must be at least $400 to reach John's goal. Therefore, we can set up the following equation:

0.02 x Total Sales ≥ $400

To solve for the minimum total sales required, we can divide both sides of the equation by 0.02:

Total Sales ≥ $400 / 0.02 Total Sales ≥ $20,000

Q: What is the minimum total sales required to reach John's goal? A: The minimum total sales required to reach John's goal is $20,000.

Q: How does John's commission affect his total sales? A: John's commission is 2% of his total sales, which means that for every $100 in sales, he earns $2 in commission.

Q: What is the relationship between John's commission and his total sales? A: The commission earned is directly proportional to the total sales. As the total sales increase, the commission earned also increases.

Q: Can John earn more than the minimum required sales? A: Yes, John can earn more than the minimum required sales. If he sells more cars or earns more commission, he will exceed his goal.

Q: What happens if John's total sales are less than the minimum required? A: If John's total sales are less than the minimum required, he will not meet his goal and will not earn the desired income.