SOLUTION: You need a 15% solution. You are going to mix 10 liters of a 27% solution with an amount of a 10% solution. How much of the 10% solution should you use?
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Question 865059: You need a 15% solution. You are going to mix 10 liters of a 27% solution with an amount of a 10% solution. How much of the 10% solution should you use? Answer by jim_thompson5910(35256) (Show Source):
We have "10 liters of a 27% solution", so we have 10*0.27 = 2.7 liters of pure alcohol.
Let x be the amount of the 10% solution we have. This amount will be in liters. So for this portion, we have 0.10x liters of pure alcohol.
Combine the two pure amounts: 2.7 + 0.10x
That's as far as you can go for that bit. We have a total of 2.7 + 0.10x liters of pure alcohol.
This is out of a total of 10+x liters of solution (10 from the first bit, x from the second)
This ratio is and this represents the fraction of pure alcohol over the total amount of solution. We want this fraction to be equal to 0.15 (15%) since we want a 15% solution at the end. So set it equal to 0.15 and solve for x
Remember that we made x equal to the amount of 10% solution we'll mix in. So because the initial problem is asking for that, we can stop here.
So we must mix in 24 liters of the 10% alcohol solution with 10 liters of the 27% alcohol solution to get a final solution of 15% alcohol.
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