"Any eighth-grade boy or girl who is 'all there' should solve it in about thirty seconds" is hyperbole (it took me a couple of minutes), but in general the public reaction to this seems like a demonstration of the Flynn effect.
Mary is twice as old as Ann was when Mary was as old as Ann is now. So we have to deduct the age difference twice from Mary's current age to find out how old Ann was when Mary was as old as Ann is now, which is half Mary's current age:
Mary is 24 years old. When Mary was Ann’s current age, Ann was 12 years old (half Mary’s current age).
This makes it a bit easier to realize that Ann’s age has to be right in the middle of 12 and 24.
Are you in the 8th grade? Those of us a couple of decades past the 8th grade are maybe slower at algebra than someone who is actively drilling it...
I can't see a way to do it without algebra.
How I understand it:
Mary is 24, Ann is a few (n) years younger
Mary is twice as old as Ann was when Mary was as old as Ann is now. So we have to deduct the age difference twice from Mary's current age to find out how old Ann was when Mary was as old as Ann is now, which is half Mary's current age: So the age difference is 6, and Ann is 18.ann_old=12
mary_curr=24
mary_old=ann_curr
mary_curr-ann_curr=X
mary_old-ann_old=X
24-ann_curr=X
mary_old-12=X
ann_curr-12=X
24-ann_curr=ann_curr-12
2ann_curr -12 = 24
2ann_curr = 36
ann_curr = 18