After how many years will you have the same salary? After 2 years.
What will that salary be? $40,000.
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]
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.
Answer:
2 years
$40,000
Step-by-step explanation:
Given information:
Define the variables
Create two equations with the given information and defined variables:
[tex]\begin{cases}y = 38000 + 1000x\\y = 24000 + 8000x\end{cases}[/tex]
To find after how many years the salary will be the same, substitute the second equation into the first equation and solve for x:
[tex]\implies 24000+8000x = 38000+1000x[/tex]
Subtract 1000x from both sides:
[tex]\implies 24000+8000x-1000x = 38000+1000x-1000x[/tex]
[tex]\implies 24000+7000x = 38000[/tex]
Subtract 24000 from both sides:
[tex]\implies 24000+7000x -24000 = 38000-24000[/tex]
[tex]\implies 7000x = 14000[/tex]
Divide both sides by 7000:
[tex]\implies \dfrac{7000x}{7000} = \dfrac{14000}{7000}[/tex]
[tex]\implies x = 2[/tex]
Therefore, the number of years after which the salaries will be the same is 2 years.
To find what the salary will be, substitute x = 2 into one of the equations and solve for y:
[tex]\implies 38000 + 1000(2) = 38000+2000=40000[/tex]
Therefore, the salary after 2 years will be $40,000.
Learn more about systems of equations here:
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