SOLUTION: How many liters of a 40% alcohol solution should be added to 40 liters of a 10% alcohol solution to obtain a 20% alcohol solution.

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Question 71575: How many liters of a 40% alcohol solution should be added to 40 liters of a 10% alcohol solution to obtain a 20% alcohol solution.
Found 2 solutions by stanbon, galactus:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How many liters of a 40% alcohol solution should be added to 40 liters of a 10% alcohol solution to obtain a 20% alcohol solution.
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40% solution DATA:
Let amt of solution be "x" liters; Amt of alcohol is 0.40x liters
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10% solution DATA:
Amt is 40 liters; amt of alcohol is 0.10(40)= 4 liters
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20% solution DATA:
Amt is "x+40" liters; amt of alcohol is 0.20(x+40)= 0.20x+8 liters
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EQUATION:
alcohol + alcohol = alcohol
0.40x+4 = 0.20x+8
0.20x=4
x=20 liters (amt of 40% solution that must be added)
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Cheers,
Stan H.

Answer by galactus(183) About Me  (Show Source):
You can put this solution on YOUR website!
These mixture problems are the bane of many a student.
Let x = the amount of 40%
0.40x%2B0.10%2840%29=0.20%28x%2B40%29
You're adding x amount of 40% to the existing 40 liters to get a 20% mix.
Therefore, we have 0.20(x+40).
Now, to solve:
0.40x%2B4=0.20x%2B8
0.20x=4
x=20 liters of 40% solution added to 40 liters of 10% will give 60 liters of 20%.