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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.

Respuesta :

Using linear functions, we have that:

A.

For Company A: [tex]S_A(n) = 31000 + 3000n[/tex]

For Company B: [tex]S_B(n) = 38000 + 2000n[/tex]

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

A linear function is given by:

[tex]y = mx + b[/tex]

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, [tex]b = 31000, m = 3000[/tex], and the salary after n years is given by:

[tex]S_A(n) = 31000 + 3000n[/tex]

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

[tex]S_B(n) = 38000 + 2000n[/tex]

Item b:

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

[tex]S_A(n) = S_B(n)[/tex]

Then

[tex]31000 + 3000n = 38000 + 2000n[/tex]

[tex]1000n = 7000[/tex]

[tex]n = \frac{7000}{1000}[/tex]

[tex]n = 7[/tex]

The salaries will be the same after 7 years.

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

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