Question

A worker has job offers from two companies. The information below summarizes the job offer from each company.Company A:Starting salary of $31,000Raise of $3000 each yearCompany B:Starting salary of $38,000Raise of $2000 each yearPart A: Write an equation in terms of n years that can be used to determine the number of years when the salaries would be the same for both companies.Part B: Use the equation you wrote in part A to determine the number of years it would take for the salaries to be the same for both companies. Use mathematics to support your answer.

Answer 1

Using linear functions, we have that:

A.

For Company A: $S_A(n) = 31000 + 3000n$

For Company B: $S_B(n) = 38000 + 2000n$

B. The salaries will be the same after 7 years.

A linear function is given by:

$y = mx + b$

In which:

• m is the slope, which is the rate of change.
• b is the y-intercept, which is the initial value.

Item a:

• For Company A, the salary starts at $31,000, with a raise of $3,000 each year. Thus, $b = 31000, m = 3000$, and the salary after n years is given by:

$S_A(n) = 31000 + 3000n$

• For Company B, the salary starts at $38,000, with a raise of $2,000 each year. Thus, $b = 38000, m = 2000$, and the salary after n years is given by:

$S_B(n) = 38000 + 2000n$

Item b:

• They will be the same after n years, for which:

$S_A(n) = S_B(n)$

Then

$31000 + 3000n = 38000 + 2000n$

$1000n = 7000$

$n = \frac{7000}{1000}$

$n = 7$

The salaries will be the same after 7 years.

A similar problem is given at brainly.com/question/24282972