SOLUTION: A solution of 79% alcohol is to be mixed with a solution of 20%alcohol to form 413 liters o a 47% solution. How many liters of the 79% solution must be used? Thank you so much for

Question 85365: A solution of 79% alcohol is to be mixed with a solution of 20%alcohol to form 413 liters o a 47% solution. How many liters of the 79% solution must be used?
Thank you so much for helping me.
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=number of liters of the 79% solution needed
Then 413-x=number of liters of 20% alcohol that must be used
Now we know that the pure alcohol in the 79% solution (0.79x) plus the amount of pure alcohol in the 20% solution(0.20(413-x)) must equal the amount of pure alcohol in the final mixture (0.47(413)). So our equation to solve is:

0.79x+0.20(413-x)=0.47(413) get rid of parens
0.79x+82.6-0.20x=194.11 subtract 82.6 from both sides
0.79x+82.6-82.6-0.20x=194.11-82.6 collect like terms
0.59x=111.51 divide both sides by 0.59
x=189 liters---------- of the 79% solution is needed
413-189=224 liters------------------of the 20% solution is needed

Ck:
0.79(189)+0.20(224)=0.47(413)
149.31+44.8=194.11
194.11=194.11

Hope this helps----ptaylor

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