How many gallons of lemonade with 35% sugar content must be added to 40 gallons of lemonade with 0.5% sugar content to obtain a mixture with 12% sugar content?

Using the rule of alligation, the percentage of sugar in the first lemonade is 35%, in the second is 0.5%, and the desired mean is 12%. The ratio of the first lemonade to the second is (12 minus 0.5) to (35 minus 12), which simplifies to 11.5 to 23, or a 1 to 2 ratio. Since the second lemonade is 40 gallons, the amount of the first lemonade needed is half of that, which is 20 gallons.

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