Andrew, I love mental math tricks like that. I don't generally top up, but I use a similar exercise to calculate the final fills with transfilling.
In my Rec Triox class, the instructor was going through an incredibly cumbersome method of calculating gas mixing, that involved taking psi and converting to cf and then back -- when I pointed out that the problem was extremely easy if you simply solved for nitrogen (whose only source was the air or Nitrox top) he was taken rather aback.


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