SOLUTION: I'm three times as old as you were when I was as old as you are now. When you will be my age, together we will be 13370 years old. How old am I?

Let M = my age now
Let Y = your age now

Change the wording "as old as you are now" to "your age".
(It's easier to see when you reduce the number words.)

Let x = the number of years ago it's been since I was your age.
(Note that this is the same as the difference in their ages.)

Then x years ago I was Y, so

M-x = Y 

and also, x years ago you were Y-x, and my age now, M, is
3 times that, or 3(Y-x).  Therefore:

M = 3(Y-x)

x years from now I will be M+x and you will be Y+x, so we
add those together and set that equal to 13370

(M+x)+(Y+x) = 13370

So we have 3 equations and 3 unknowns:



Solve that system and you get:

M=5730, Y=3820, x=1910 

So I am 5730 years old.  (Pretty old, so tell us how the pyramids
were built! ha ha)

---------------------------

That checks because:

I am 1910 years older than you. (Because 5730-3820=1910)

Therefore 1910 years ago I was your age, (Because 5730-1900=3820),
and you were 1910. (Because 3820-1910=1910).

I am now 3 times that (Because 1910 times 3 is 5730).

1910 years from now you will be 5730 (Because 3820+1910=5730, my age),
and I will be 7640 (Because 5730+1910=7640).

And together we will be 13370 years old. (Because 7640+5730=13370).

I have a hunch the number 13370 was copied wrong.  Use the correct
number and solve it as above.

Edwin