The analysis I presented was correct but I did leave out the amount in the replacement water. basically the final value is increased by whatever is in the replacement water.

final value before water change=(change between water chang)/(fraction of water change)+amount in replacement water

This is a "fun" exercise but what it is really supposed to "spark" are some questions.

1) can water changes at "normal" (whatever that is) really maintain an aquarium.

2) Or is the real problem to solve to get the buildup down to 0.

To me it is the later. But perhaps you-all can chime in. (I am in the south. )

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fw leiden since 1979, fo salt since 1979, mixed reef 55g 2002-2009. Strong emphasis on the tank taking care of itself. Balanced with plant life, no water changes, tap water, no filters in FW. Only dosing calcium, alk, mag in marine reef tanks. http://www.aquariumforum.com/f15/my-...ods-26410.html
recent tanks (till 2009) 7 years- 10g FW leiden 7 yrs, 55g mixed reef 7, 2 yrs, 20g FW leiden, 10 g fw leiden , 29g mixed reef, current tank 55g leiden