We need to find how many bottles until total volume filled does not exceed 729? But total volume is fixed.
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- So: How many bottles needed to hold 729 ml, each next holds half of the *previous* bottle’s capacity?
- But that leads to: \(729 + 364.5 + 182.25 + \dots\) → sum > 729.
- Correct interpretation from context: The solution is poured sequentially into new bottles, each with half the capacity of the prior used bottle. Start with full 729 ml in first bottle (capacity 729). Next bottle capacity: 364.5, then 182.25, etc.
- Actually: The total volume is 729 ml, and we fill progressively into successively smaller bottles.
- But we stop when we can't fill completely?
- But the question asks: "how many bottles will be needed to fill the entire solution?"
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