Answer: 8 years for her salary to be the same at both companies.
Explanation:
To solve this problem, we can set up a system of linear equations to represent the salaries at each company. Let's say that the first company's salary is represented by the variable x, and the second company's salary is represented by the variable y. Since the first company offers a starting salary of $28,000 with a raise of $3,000 each year, we can represent this with the equation x = 28,000 + 3,000 * t, where t represents the number of years. Similarly, the second company offers a starting salary of $36,000 with a raise of $2,000 each year, so we can represent this with the equation y = 36,000 + 2,000 * t.
Since we want to find the number of years it will take for Joanne's salary to be the same at both companies, we can set the two equations equal to each other and solve for t:
x = 28,000 + 3,000 * t
y = 36,000 + 2,000 * t
x = y
28,000 + 3,000 * t = 36,000 + 2,000 * t
We can solve this equation by combining like terms on both sides of the equation:
28,000 + 3,000 * t = 36,000 + 2,000 * t
-8,000 = -1,000 * t
Dividing both sides of the equation by -1,000, we get:
8,000 = t
Thus, it will take Joanne 8 years for her salary to be the same at both companies.