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Answer :
Final answer:
The problem describes a situation involving solution mixtures where the concentration of the spirit changes after a portion of the bottle's content is replaced. The butler took 4/3 of the bottle.
Explanation:
The problem asked here is mathematical, related to proportions and alcohol concentration in solutions. Let's denote x as the fraction of the bottle that the butler stole. Therefore, from the problem, we can set up the following relationship:
0.32*(1 - x) + 0.18*x = 0.24
32% of the original wine that remained in the bottle added with the 18% spirit from what the butler replaced is equal to 24% of the new mixture.
solving the equation gives us: x = 0.32 - 0.24 = 0.18 - 0.24. Hence, x = 8/6 = 4/3. So, the butler took 4/3 of the bottle.
Learn more about Mixture Problems here:
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