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Anonymous at Tue, 29 Oct 2024 15:22:08 UTC No. 16454821

Math question for puzzle solvers

Consider using a single cup for tea, and you never swap the cup.
Instead of completely finishing up the tea, you generally drink until some of the tea ends up cold, leaving a fraction of the tea left. Instead of dumping the tea and replacing it with new cold water, you keep that tea in there while throwing the teabag and placing a new teabag, and then filling up the rest of the cup with new boiling water for the remainder.
Conretely, with raw numbers, as an example you would drink your cup of tea until 20% remains, you will then throw the tea bag and replace it with a new, and place 80% of the cup with new boiling water, meaning 20% is tea and 80% is new boiling water.

If you do this an infinite amount of times, what % of the cup will be tea versus fresh water? For any given fraction left undrank, although it is always the same fraction X that is left undrank. Do not consider any physical factors such as evaporation