SOLUTION: Two vessels contain mixture of alcohol and water. In one there is three times as much as alcohol as water; in the other, five times as much water as alcohol. How much must be drawn

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Question 767063: Two vessels contain mixture of alcohol and water. In one there is three times as much as alcohol as water; in the other, five times as much water as alcohol. How much must be drawn off from each to fill a third vessel which holds 7 gallons, in order that its contents may be half alcohol and half water?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of mixture to be drawn off
from the 3:1 alcohol to water mixture
Let +b+ = gallons of mixture to be drawn off
from the 1:5 alcohol to water mixture
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+3%2F4+ of +a+ will be alcohol
+1%2F6+ of +b+ will be alcohol
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(1) +a+%2B+b+=+7+
(2) +%28+%283%2F4%29%2Aa+%2B+%28+1%2F6%29%2Ab+%29+%2F+7+=+.5+
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(2) +%28+%283%2F4%29%2Aa+%2B+%28+1%2F6%29%2Ab+%29+=+3.5+
Multiply both sides by +12+
(2) +9a+%2B+2b+=+42+
Multiply both sides of (1) by +2+ and
subtract (1) from (2)
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I have to run- solve for +a+%5D%5D%5D+and+%7B%7B%7B+b+