SOLUTION: A 100 liter barrel of vinegar is 8% acetic acid. Before it can be bottled and used in cooking, the acidity must be reduced to 5% by diluting it with pure water. In order to produce

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A 100 liter barrel of vinegar is 8% acetic acid. Before it can be bottled and used in cooking, the acidity must be reduced to 5% by diluting it with pure water. In order to produce      Log On

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Question 884450: A 100 liter barrel of vinegar is 8% acetic acid. Before it can be bottled and used in cooking, the acidity must be reduced to 5% by diluting it with pure water. In order to produce 64 liters of usable vinegar, how many liters of vinegar from the barrel and how many liters of pure water should be combined?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = liters of 8% acetic acid from the barrel needed
Let +b+ = liters of pure water to be added
+.08a+ = liters of acetic acid taken from the barrel
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(1) +a+%2B+b+=+64+
(2) +.08a+%2F+64+=+.05+
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(2) +.08a+=+.05%2A64+
(2) +a+=+3.2+%2F+.08+
(2) +a+=+40+
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(1) +40+%2B+b+=+64+
(1) +b+=+24+
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40 liters of vinegar from the barrel and 24 liters
of pure water should be combined
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check:
(2) +.08%2A40+%2F+64+=+.05+
(2) +3.2%2F64+=+.05+
(2) +3.2+=+.05%2A64+
(2) +3.2+=+3.2+
OK