Question

Nina is 10 years younger than Deepak. Deepak is 3 times as old as Nina. Which system of equations can be used to find d, Deepak's age, and n, Nina's age?

A) d = n + 10 d = 3n
B) d = n − 10 d = 3n
C) d = n + 10 n = 3d
D) d = n − 10 n = 3d

Answer 1

The answer is A. Deepak is 10 years older than Nina, so it cancels out B and D. And Deepak is 3 times Nina's age, not the other way around.

Answer 2

The first thing we must do for this case is to define variables.

We have then:

n: Age of Nina

d: Age of Deepak

We now write the system of equations that models the problem.

Nina is 10 years younger than Deepak:

`image`

Deepak is 3 times as old as Nina:

`image`

Therefore, the system of equations is given by:

`image`

Answer:

A system of equations that are used to find d, Deepak's age, and n, Nina's age is:

A) d = n + 10; d = 3n