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I think it’s easier to see if you drop the time indices and just introduce a variable for the elapsed time. So:

Mary := 24 = 2(A - Δ)

A = Mary - Δ

And then it’s just substitution. But of course what appeals to one’s intuition is very personal



To me, explicitly representing the two pairs of ages (now: M, A; previously: M', A') is simpler because it let's you directly represent the problem statement without any mental gymnastics whatsoever.

  M = 2A' "Mary is [now] twice as old as Ann was ..."

  M'= A   "when Mary was as old as Ann is now"




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