Brenda has a job offers at two companies. One company offers a starting salary of $75,000 with a raise of $2,500 each year. The 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 ?

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carlosego carlosego · Answer 1 · 2018-07-28T15:10:32+02:00

For this case, the first thing we must do is define variables.

We have then:

x: number of years

y: total salary

For company 1 we have:

[tex] y = 2500x + 75000
[/tex]

For company 2 we have:

[tex] y = 5000x + 55000
[/tex]

By the time both salaries are equal we have:

[tex] 2500x + 75000 = 5000x + 55000
[/tex]

From here, we clear the value of x.

We have then:

[tex] 5000x - 2500x = 75000 - 55000

2500x = 20000
[/tex]

[tex] x = \frac{20000}{2500}

x = 8
[/tex]

Answer:

Brenda's salary would be the same with both companies in 8 years.