Given the scenario where Nahil and Mae work at the same company, we have two pieces of information:
1. Nahil has been at the company 5 times as long as Mae.
2. Nahil's time at the company is 8 more than 3 times Mae's time.
These statements can be converted into the following system of equations:
[tex]\[
\begin{aligned}
x &= 5y \\
x &= 8 + 3y
\end{aligned}
\][/tex]
Here, [tex]\(x\)[/tex] represents Nahil's time at the company, and [tex]\(y\)[/tex] represents Mae's time at the company.
### Step-by-Step Solution:
1. Set the equations equal to each other:
Since both equations equal [tex]\(x\)[/tex], we can set the right-hand sides equal to each other:
[tex]\[
5y = 8 + 3y
\][/tex]
2. Solve for [tex]\(y\)[/tex]:
To isolate [tex]\(y\)[/tex], subtract [tex]\(3y\)[/tex] from both sides of the equation:
[tex]\[
5y - 3y = 8
\][/tex]
Simplifying this, we get:
[tex]\[
2y = 8
\][/tex]
Next, divide both sides by 2:
[tex]\[
y = \frac{8}{2} = 4
\][/tex]
So, Mae has been at the company for 4 years.
3. Find Nahil's time ( [tex]\(x\)[/tex] ):
Now that we know [tex]\(y = 4\)[/tex], we can substitute this value into either of the original equations to find [tex]\(x\)[/tex]. Using the first equation:
[tex]\[
x = 5y
\][/tex]
Substitute [tex]\(y = 4\)[/tex]:
[tex]\[
x = 5 \cdot 4 = 20
\][/tex]
So, Nahil has been at the company for 20 years.
### Conclusion:
Nahil has been with the company for 20 years, while Mae has been there for 4 years. Therefore, the correct answer is:
Nahil has been with the company for 20 years, while Mae has been there for 4 years.
