Question

Corey earns $50 for each insurance policy he sells plus $500 each week. Maria earns $25 for each policy she sells plus $250 each week. Write an inequality to show how many policies each employee will need to sell so that Maria earns the same or more than Corey.

Answer 1

The inequality to show how many policies Maria needs to sell to earn the same or more than Corey is 25x + 250 ≥ 50x + 500. Upon solving, it's determined Maria cannot out-earn Corey based on policy sales as it would require her to sell a negative number of policies, which is impossible.

Step-by-step explanation:

To determine how many policies each employee needs to sell so that Maria earns the same or more than Corey, we can set up an inequality that represents their earnings. Let x be the number of policies sold by each. Corey earns $50 per policy plus a weekly base of $500, so his earnings can be represented as 50x + 500. Maria earns $25 per policy plus a weekly base of $250, so her earnings can be represented as 25x + 250. The inequality will show Maria's earnings being greater than or equal to Corey's earnings, which translates to:

25x + 250 ≥ 50x + 500

Now we need to solve for x:

• Subtract 25x from both sides: 250 ≥ 25x + 500
• Subtract 500 from both sides: -250 ≥ 25x
• Divide both sides by 25: -10 ≥ x

This result indicates that, with the current payment structure, Maria cannot earn the same or more than Corey based on sales alone since Maria would need to sell a negative number of policies, which is impossible. Therefore, Maria can never earn more than Corey on the basis of policies sold.