Answers:
After how many years will you have the same salary? After 2 years.
What will that salary be? $40,000.
Step-by-step explanation:
1. Find equations for each company's salary.
Let's create equation that give the salary with respect to time.
For company A, the function of salary is:
[tex]S(t)=1000x+38000[/tex], where x is the time in years.
For company B, the function of salary is:
[tex]S(t)=8000x+24000[/tex], where x is the time in years.
2. Create a system of equations.
For this questions, we must set up a system of linear equations to see where the 2 lines of these equations meet. This will give us the point where both salary and time are the same in the 2 companies.
[tex]\left \{ {{S(t)=1000x+38000} \atop {S(t)=8000x+24000}} \right.[/tex]
3. Solving the system of equations,
a. Write the functions in terms of x and y.
[tex]1.y =1000x+38000\\ \\2. y=8000x+24000[/tex]
b. Equal the expressions.
[tex]1000x+38000=8000x+24000[/tex]
c. Solve for x.
[tex]1000x+38000=8000x+24000\\ \\1000x-8000x=24000-38000\\ \\-7000x=-14000\\ \\x=\frac{-14000}{-7000} \\ \\x=2[/tex]
d. Use the x value in any of the functions to obtain y.
[tex]y=8000(2)+24000\\ \\y=40000[/tex]
4. Interpret the results.
The point where the 2 functions meet is (2,40000), this means that 2 years after the person joins any of the companies they will have the same salary. This salary will be $40,000.
