SOLUTION: Roman mixes 12 liters of 8% acid solution with a 20% acid solution, which results in a 16% acid solution. Find the number of liters of 20% acid solution in the new mixture.

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Question 254095: Roman mixes 12 liters of 8% acid solution with a 20% acid solution, which results in a 16% acid solution. Find the number of liters of 20% acid solution in the new mixture.
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=the number of liters of the 20% solution in the new mixture
Now we know that the amount of pure acid in the 8% solution (0.08*12) plus the amount of pure acid in the 20% solution (0.20x) has to equal the amount of pure acid in the new mixture (0.16(12+x)). So our equation to solve is:
0.08*12+0.20x=0.16(12+x) get rid of parens and simplify
0.96+0.20x=1.92+0.16x subtract 0.16x and also 0.96 from each side
0.96-0.96+0.20x-0.16x=1.92-0.96+0.16x-0.16x collect like terms
0.04x=0.96 divide each side by 0.04
x=24 liters----------------------amount of 20% solution needed
CK
0.08*12+0.20*24=0.16(12+24)
0.96+4.8=5.76
5.76=5.76
Hope this helps---ptaylor