In a mixture, there are 2 parts methane and 5 parts ethane. How much mixture (in litres) should we draw and replace with methane so that the mixture contains methane and ethane in the same amount?

The total mixture is 7 litres, and you want the ethane to be 50 percent, meaning the final ethane amount must be 3.5 litres. The final ethane amount is 5 times the fraction of mixture remaining, so 5 times (1 minus the replaced fraction) equals 3.5. Solving this gives a remaining fraction of 0.7, meaning 30 percent of the 7 litres, which is 2.1 litres, must be drawn and replaced.

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