SOLUTION: is it possible to mix a 20% sugar solution with a 40% sugar solution to get a 60% sugar solution?

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No.
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To increase the solution to 60% sugar, you would have to add either pure sugar (100% sugar) or a solution that is more than 60%.
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That is because no matter how much 20% solution and 40% you add together, the maximum solution will be achieved with zero 20% solution and the rest being 40% solution. The maximum is 40% solution.
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Think about the average. There is no way for the average of 20 and 40 to be 60.
It has to be somewhere between 20 and 40.
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If you could add pure sugar (100% sugar), you would set up the equation as:
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40%(x) + 100%(y) = 60%(x+y)
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