SOLUTION: A mixture contains alcohol and water in the ratio 4:3. If 7 litres of water is added to the mixture, the ratio of alcohol and water becomes 3:4. Find the quantity of alcohol in the

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A mixture contains alcohol and water in the ratio 4:3. If 7 litres of water is added to the mixture, the ratio of alcohol and water becomes 3:4. Find the quantity of alcohol in the      Log On

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Question 201890: A mixture contains alcohol and water in the ratio 4:3. If 7 litres of water is added to the mixture, the ratio of alcohol and water becomes 3:4. Find the quantity of alcohol in the mixture ?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = liters of alcohol in original mixture
Let w = liters of water in original mixture
given:
(alcohol in original mixture)/(water in original mixture) = 4/3
a%2Fw+=+4%2F3
Multiply both sides by 3w
3a+=+4w
w+=+%283%2F4%29%2Aa liters
a+%2F+%28%283%2F4%29%2Aa+%2B+7%29+=+3%2F4
Multiply both sides by %283%2F4%29%2Aa+%2B+7
a+=+%283%2F4%29%2A%28%283%2F4%29%2Aa+%2B+7%29
a+=+%289%2F16%29%2Aa+%2B+21%2F4
16a+=+9a+%2B+84
7a+=+84
a+=+12
There are 12 liters of alcohol in the mixture
check:
a+%2F+%28%283%2F4%29%2Aa+%2B+7%29+=+3%2F4
12+%2F+%28%283%2F4%29%2A12+%2B+7%29+=+3%2F4
12+%2F+%289+%2B+7%29+=+3%2F4
12%2F16+=+3%2F4
3%2F4+=+3%2F4
OK