Donovan has offers for two sales jobs. Job A pays a base total earnings of 35,000 plus a 11% commission on sales. Job B pays a base total earnings of 40,000 plus 7% commission on sales. How much would Donovan have to sell for the total earnings from Job A to exceed the total earnings from Job B?

Round to the nearest dollar.

Let's set up the problem algebraically.

Let $ x $ represent the total sales Donovan makes.

- **Total earnings from Job A** is the base salary of 35,000 plus 11% commission on sales:
  \[
  E_A = 35,000 + 0.11x
  \]

- **Total earnings from Job B** is the base salary of 40,000 plus 7% commission on sales:
  \[
  E_B = 40,000 + 0.07x
  \]

We want to find the value of $ x $ such that the total earnings from Job A exceed the total earnings from Job B:
\[
35,000 + 0.11x > 40,000 + 0.07x
\]

Now, let's solve this inequality:

\[
35,000 + 0.11x > 40,000 + 0.07x
\]

First, subtract $ 0.07x $ from both sides:

\[
35,000 + 0.04x > 40,000
\]

Now, subtract 35,000 from both sides:

\[
0.04x > 5,000
\]

Finally, divide both sides by 0.04 to isolate $ x $:

\[
x > \frac{5,000}{0.04} = 125,000
\]

Therefore, Donovan would have to sell more than **$125,000** for the total earnings from Job A to exceed the total earnings from Job B.

Would you like more details on any part of the solution?

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Here are 5 related questions for you:
1. How would the solution change if the commission rates for both jobs were different?
2. What if Job A offered a bonus after a certain sales threshold?
3. How does the difference in base salaries influence Donovan's decision?
4. What happens if Donovan has a sales target in both jobs, how would that affect his choice?
5. How can Donovan predict which job will be better if he knows his estimated annual sales?

**Tip:** When comparing different job offers, it's helpful to calculate break-even points for different scenarios to ensure you're making the best financial decision!

Donovan has offers for two sales jobs. Job A pays a base total earnings of 35,000 plus a 11% commission on sales. Job B pays a base total earnings of 40,000 plus 7% commission on sales. How much would Donovan have to sell for the total earnings from Job A to exceed the total earnings from Job B?

Learn how to compare two sales job offers by using algebra to solve inequalities. This example calculates how much Donovan needs to sell for Job A, with a base salary of $35,000 and 11% commission, to surpass the total earnings from Job B, which offers a base salary of $40,000 and 7% commission. Ideal for students in Grades 8-10.

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