Problem: When one ounce of water is added to a mixture of acid and water, the new mixture is acid. When one ounce of acid is added to the new mixture, the result is acid. The percentage of acid in the original mixture is
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Solution:
Let denote the number of ounces of (water, acid) originally. After addition of oz. Water and oz. acid we have respectively and oz. of acid in mixtures totaling and oz. Which means that and . These yield from which the percentage of acid originally was .