Question

Nikhil and Mae work at the same company. Nikhil has been at the company 5 times as long as Mae. Nikhil's time at the company is 8 more than 3 times Mae's time. The following system of equations models the scenario:

x = 5y
x = 8 + 3y

How many years has each person been employed by the company?

Nikhil has been with the company for 15 years, while Mae has been there for 3 years.
Nikhil has been with the company for 20 years, while Mae has been there for 4 years.
Nikhil has been with the company for 25 years, while Mae has been there for 5 years.
Nikhil has been with the company for 30 years, while Mae has been there for 6 years.

Answer 1

The answer is B. Nikhil has been with the company for 20 years, while Mae has been there for 4 years.

Explanation:

We have the system of equations:

x = 5y

x = 8 + 3y

We can solve for x in terms of y in the second equation:

x = 8 + 3y

x - 3y = 8

Now we can substitute the first equation into this equation to solve for y:

x - 3y = 8

5y - 3y = 8

2y = 8

y = 4

So Mae has been employed by the company for 4 years. We can now substitute this value of y into the first equation to solve for x:

x = 5y

x = 5(4)

x = 20

So Nikhil has been employed by the company for 20 years.

Therefore, the answer is B. Nikhil has been with the company for 20 years, while Mae has been there for 4 years.

Answer 2

Nikhil has been with the company for 20 years, while Mae has been there for 4 years.

Explanation:

equate both x's to each other:

5y = 8+3y

2y=8

y=4 (this is the number of years for Mae)

For Nikhil it is 5 times 4 = 20 years