Question

VSalesperson A receives 9 bonuses per year, and Salesperson B receives 6 bonuses per year. Each bonus received by Salesperson B is $2,000 more than the bonus received by Salesperson A. The total amount in dollars for all bonuses received by Salesperson A is $3,000 less than the total amount in dollars for all bonuses received by Salesperson B. Which system of equations can be used to find a, the amount in dollars of each bonus received by Salesperson A, and b, the amount in dollars of each bonus received by Salesperson B.

a = b + 2,000
9a = 6b - 3,000

Answer 1

To solve for Salesperson A's and B's bonus amounts, the correct system of equations is b = a + 2000 and 9a + 3000 = 6b, based on the information provided about the differences in their bonuses and total amounts received per year.

Step-by-step explanation:

To find a system of equations that can be used to find a, the amount in dollars of each bonus received by Salesperson A, and b, the amount in dollars of each bonus received by Salesperson B, we need to set up two equations based on the information given:

• Salesperson B receives a bonus that is $2,000 more than Salesperson A's bonus.
• The total amount of bonuses for Salesperson A is $3,000 less than that of Salesperson B.

Let a represent the amount of Salesperson A's bonus and b represent the amount of Salesperson B's bonus. From the first piece of information, we can write the equation:

b = a + 2000

For the second part, we know that Salesperson A receives 9 bonuses a year and Salesperson B receives 6 bonuses a year. Since the total amount for Salesperson A's bonuses is $3,000 less, we write:

9a + 3000 = 6b

Therefore, the correct system of equations to solve for a and b is:

• b = a + 2000
• 9a + 3000 = 6b