SOLUTION: One gallon container is full of a 75% alcohol solution. How much must be drained off and replaced by a 50% alcohol solution to produce one gallon of 65% alcohol solution?

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Question 486071: One gallon container is full of a 75% alcohol solution. How much must be drained off and replaced by a 50% alcohol solution to produce one gallon of 65% alcohol solution?
Found 2 solutions by jorel1380, lwsshak3:
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
1x.65=.65
.75n+(.75-.5)(1-n)=.65
.75n+.25-.25n=.65
.5n=.40
n=.40/.5=.8
1-n=.2
.75(.8)=.6
+.25(.2)=.05
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"""""""".65
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.2 gallons must be drained off and replaced by .50 alcohol to make the mix..

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
One gallon container is full of a 75% alcohol solution. How much must be drained off and replaced by a 50% alcohol solution to produce one gallon of 65% alcohol solution?
***
let x=gal of 75% solution to be drained and replaced by a 50% solution.
1-x= gal of 75% solution remaining.
..
75%(1-x)+50%(x)=65%(1)
.75-.75x+.5x=.65
-.25x=-.10
x=0.4 gal
ans:
0.4 gal of 75% solution must be drained and replaced by a 50% solution to produce one gallon of 65% alcohol solution