Age questions: How to approach solving this?

Question

Completely foxed by this question: Moses is twice as old as Methusaleh was when Methusaleh was one-third as old as Moses will be when Moses is as old as Methuselah is now. The difference in their ages is 666 years. How old is Methusaleh now?

My problem is that if Methusaleh was 1/3 as old as Moses was, how come Moses age is twice that of Methusaleh? That does not now seem to make sense... Any help appreciated...

Answer 1

Notice "as old as Moses will be when Moses will be as old as X" is just a convoluted way of saying "X".

So "Moses is twice as old as Methusaleh was when Methusaleh was one-third as old as (Moses will be when Moses is as old as Methuselah is now)" = "Moses is twice as old as Methusaleh was when Methusaleh was one-third as old as (Methusalah)"

Likewise "as old as Methusaleh was when Methusaleh was X" is just a convoluted way of saying "as old as X".

So "Moses is twice as old as (Methusaleh was when Methusaleh [was one-third as old as (Methusalah)])"= "Moses is twice as old as (one third as old as Methusalah)"

So if Moses is $A$ and Methusalah is $B$ then $A = 2*\frac 13 B$. That is all this very convoluted sentence says.

THe next sentence "The difference in their ages is 666 years" is, I hope straight forward: $|B- A| = 666$. English language, but not math, implies $B > A$ but...

So solve $A = 2*\frac 13 B$ and $|B-A| = 666$.

Answer 2

Let $x$ be Moses age and $y$ be Methusaleh age now.

The system to solve is

$$y=x+666, x=2y/3$$ The solution is $$ x=1332, y=1998$$ Thus the answer is $1998$