contestada

Brenda has job offers at two companies. One company
offers a starting salary of $75,000 with a raise of $2,500 each year. The other company offers a starting salary of $55,000 with a raise of $5,000 each year. In how many years would Brenda's salary be the same with both companies? What will the salary be?

Respuesta :

Let's start by setting up equations for Brenda's annual salary at each company as a function of the number of years worked.

For the first company, Brenda's salary after working for y years would be:

S_1(y) = 75,000 + 2,500y

For the second company, Brenda's salary after working for y years would be:

S_2(y) = 55,000 + 5,000y

To find the number of years it would take for Brenda's salaries at the two companies to be equal, we can set the two equations equal to each other and solve for y:

S_1(y) = S_2(y) :

75,000 + 2,500y = 55,000 + 5,000y

20,000 = 2,500y

y = 8

So, Brenda's salaries at the two companies would be equal after 8 years.

To find out what the salary would be at that point, we can substitute y = 8 into either equation. Let's use S_1:

S_1(8) = 75,000 + 2,500(8) = 95,000

Therefore, after 8 years, Brenda's salary would be $95,000 at both companies.