SOLUTION: how many liters of pure alcohol must be added to 5 liters of a 15% alcohol solution to make a 25% solution?

Question 242341: how many liters of pure alcohol must be added to 5 liters of a 15% alcohol solution to make a 25% solution?

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of pure alcohol needed
Now we know that the amount of pure alcohol added (x) plus the amount of pure alcohol in the 5 liters((0.15)*5) has to equal the amount of pure alcohol in the final mixture ((0.25)*(5+x)). So our equation to solve is:
x+0.15*5=0.25(5+x) get rid of parens and simplify
x+0.75=1.25+0.25x subtract 0.25x and also 0.75 from each side
x-0.25x+0.75-0.75=1.25-0.75+0.25x-0.25x collect like terms
0.75x=0.50 divide each side by 0.75
x=2/3 liter------------amount of pure alcohol needed
CK
Now we'll deal in fractions
pure alcohol before they are mixed=pure alcohol after they are mixed
2/3 + 3/4 =(1/4)(5+2/3)
8/12 + 9/12=(1/4)(17/3)
17/12 = 17/12
Hope this helps---ptaylor
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