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17 Feb 2025, 05:12
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Alex3566
The term 0.5(1 - x) represents the amount of alcohol left after removing a fraction x of the original solution.
- The original solution is 1 liter, with 50% alcohol, meaning 0.5 liters of alcohol initially.
- When x liters are removed, the remaining solution is (1 - x) liters.
- Since this remaining solution is still 50% alcohol, the amount of alcohol left is 0.5 * (1 - x).
18 Apr 2025, 07:32
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A different approach to- If a fraction of a 50% alcohol solution is replaced with 25% alcohol solution, resulting in a final solution with 30% alcohol, what is the fraction of the original solution that was replaced?
Since we know that a specific amount of alcohol soln is removed from 50% alcohol soln and then added back from 25% alcohol soln- the amount (lets say x ml removed and then added) is the same- just the concentration of the solution will change. Using the weighted approach-
50% -----------30%---------------25%
distance ratio - 4 : 1
therefore, 4/5 i.e 80% replaced
Since we know that a specific amount of alcohol soln is removed from 50% alcohol soln and then added back from 25% alcohol soln- the amount (lets say x ml removed and then added) is the same- just the concentration of the solution will change. Using the weighted approach-
50% -----------30%---------------25%
distance ratio - 4 : 1
therefore, 4/5 i.e 80% replaced
