Question

Hector and Summer were both hired by the same company at the same time. Summer was promised a starting salary of $40,000 with a $1,500 raise every year. Hector's starting salary was $36,000 with a $2,000 raise every year. How many years will each coworker work at the company before Hector and Summer have the same salary?

Answer 1

Hector and Summer will have the same salary after 8 years of working at the company. This was calculated by setting up an equation with their respective starting salaries and annual raises, and solving for the number of years until the salaries are equal.

Step-by-step explanation:

To find out how many years it will take for Hector and Summer to have the same salary, we can set up an equation where Hector's starting salary, raises, and years worked equal Summer's respective salary, raises, and years worked.

Let's denote the number of years it will take for their salaries to match as 'x'. For Summer, the salary after x years can be modeled as: $40,000 + $1,500x. For Hector, the salary after x years can be modeled as: $36,000 + $2,000x.

We can set these equations equal to each other to solve for x:

$40,000 + $1,500x = $36,000 + $2,000x

After arranging the equation, we get $4,000 = $500x, and by dividing both sides of the equation by $500, we find that x = 8.

So, Hector and Summer will earn the same salary after 8 years of working at the company.