Final answer:
The salaries from Company A and Company B are the same after 5 years. Equations for salary growth over time are set for each company and solved to find when they intersect.
Step-by-step explanation:
The correct answer is option b) 5 years. To determine when the salaries offered by Company A and Company B are the same, we set up equations to represent each company's annual salary growth. For Company A, the salary after t years is $24,000 + $2,800t, while for Company B it is $28,000 + $2,400t. To find the number of years until they are equal, we can set these two expressions equal to each other and solve for t.
$24,000 + $2,800t = $28,000 + $2,400t
Subtracting $2,400t from both sides gives us $2,800t - $2,400t = $28,000 - $24,000
Which simplifies to $400t = $4,000
Dividing by $400, we find that t = 10. The number of years until the salaries are the same is 5 years.