I need help solving a linear equations story problem?

Question

The problem is: Ten years from now A will be twice as old as B. Five years ago A was three times as old as B. What are the present ages of A and B?

 

I am so confused and have been struggling. I am not sure where to even start with this.

Answer 1

Let x = A's age now

      y = B's age now

 

A's age in ten years  = 2(B's age in ten years).

 

 So, x + 10 = 2(y + 10)

 

A's age 5 years ago = 3(B's age 5 years ago)

 

So, x - 5 = 3(y - 5)

 

We have:  x + 10 = 2y + 20

    and       x - 5   = 3y - 15 

 

Subtracting the equations, we get 15 = -y + 35.

So, y = 20

 

Substituting for y into x + 10 = 2y + 20

we obtain x + 10 = 60.  Therefore, x = 50.

 

Answer:  A is 50 years old and B is 20 years old