SOLUTION: I am three times as old as you were when I was as old as you are now. When you get to be my age, together our ages will be 84. How old are you now?

I am I years old
You are Y years old.
I am X years older than you.

So the first equation is I = Y + X

I was as old as you were X years ago, and X years ago, 
you were Y - X. So I = 3(Y - X) is the second equation. 

You will get to be my age X years from now.  Then you 
will be I years old, and I will be I + X years old, and 
together our ages will be 84.  So the third equation is 
I + (I + X) = 84.

Therefore the system of three equations in three 
unknowns is

I = Y + X  
I = 3(Y - X)
I + (I + X) = 84

Solve that system and get I = 36, Y = 24, and X = 12.

Checking:

I am 36, which is three times as old as you were when I was as old 
as you are now, which was 12 years ago when I was 24 and you were 12.
And indeed my present age of 36 is 3 times 12. When you get to be my
age, 36, which will be 12 years from now, you will be 36 and I will be
48, and together our ages will be 84 because 36+48 = 84.  

So it checks.

Edwin