Comment by zephen

> Sorry to say, the first half of this comment is almost gibberish.

In what way?

> It became algebra when I introduced an unknown variable and wrote down an equation.

But a lot of people, including me, can solve it without writing down any equation.

> I can't see a way to solve the problem without doing that.

Ah. So it's gibberish because of your limitations? That's... not how this usually works. (Although, to be fair, it's often the case that people of limited intellectual means lash out with unkind comments such as "gibberish" so maybe this is how it works.)

> How did you get this equation from the problem statement?

"Mary is 24 years old. She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?"

We know that there is a delta between Mary's current age (24) and what I called X in my previous comment (Ann's current age AKA Mary's prior age). That would be 24 - X.

We also know that at some previous time, Ann was 12 (half of 24) when Mary was (Ann's current age AKA Mary's prior age).

Some of us just take the mental shortcut that the in between age has to be the average of 24 and 12 (because the delta doesn't change[1], so the delta must have been the same before as it is now), but if forced to write it down into algebra, we can say that this second statement is X - 12.

And then of course, again, because the delta doesn't change, and the delta is equal to both x-12 and 24-x, those expressions must be equal to each other.

[1] Except of course, the delta could wobble a bit for birthdays being on different dates within the year. In simple puzzles like this, of course, that +/- 1 year possibility is usually ignored.