Company a offers a starting salary of $28,000 with a raise of $3,000 each year. company b offers a starting salary of $36,000 with a raise of $2,000 per year. company c offers a starting salary of $18,000. after how many years would the salaries for companies a and b be the same? how much of a raise per year would company c have to offer to equal the salaries of companies a and b in the year in which the salaries of companies a and b in the year in which the salaries of those two companies are the same?

Starting salary offered by Company A = $28000
Amount of raise per year given by Company A per year = $3000
Starting salary offered by Company B =$36000
Amount of raise per year given by Company B = $2000
Let us assume the number of years after which the salary offered by Company A will be the same as Company B = x
Then
28000 + 3000x = 36000 + 2000x
3000x - 2000x = 36000 - 28000
1000x = 8000
x = 8000/1000
   = 8 years
So from the above deduction we can conclude that after 8 years the salary of Company A and Company B will become equal.
More information's are also provided for the second part of the question.
Starting salary offered by Company C = $18000
Let us assume the amount of raise per year given by Company C = z dollars
Number of years in which the salaries of Company C will become equal to the salaries of Company A and B = 8 years
Then
18000 + 8z = 28000 + (3000 * 8)
18000 + 8z = 28000 + 24000
18000 + 8z = 52000
8z = 52000 - 18000
8z = 34000
z = 34000/8
   = 4250 dollars
From the above deduction we can conclude that the raise given by Company C should be $4250.