SOLUTION: I would like the formula to solve solution mixture problems. For example: An alchemist wants to mix an 85% alcohol solution with 30 liters of 30% alcohol solution to get a new solu

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Question 879794: I would like the formula to solve solution mixture problems. For example: An alchemist wants to mix an 85% alcohol solution with 30 liters of 30% alcohol solution to get a new solution that is 45% alcohol. How much of the 85% alcohol solution should be added to balance this equation?
I can work out the problem if I had the formula so that I can plug in the numbers. Please help...thank you for ypur time and consideration
Amber
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We have "30 liters of 30% alcohol solution"

So we have 30*0.30 = 9 liters of pure alcohol.


We want to mix in some unknown amount of an 85% alcohol solution. Let's say we add x liters of this 85% solution.

That would mean we are adding in 0.85x liters of pure alcohol.


So we now have 9 + 0.85x liters of pure alcohol.

This is the total amount of pure alcohol.

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There are 30 liters of the 30% solution and x liters of the 85% solution. So in total, we have 30+x liters of the mixed stuff (water+alcohol+other stuff).

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Divide the total amount of pure alcohol by the total amount of solution:

(total amount of pure alcohol)/(total amount of solution) = (9 + 0.85x)/(30 + x)

The expression (9 + 0.85x)/(30 + x) represents the percentage of the final solution that is pure alcohol. We want this percentage to be 45%, so we set it equal to 0.45 to get

(9 + 0.85x)/(30 + x) = 0.45

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Now solve for x


(9 + 0.85x)/(30 + x) = 0.45


9 + 0.85x = 0.45(30 + x)


9 + 0.85x = 13.5 + 0.45(x)


9 + 0.85x = 13.5 + 0.45x


0.85x = 13.5 + 0.45x - 9


0.85x - 0.45x = 13.5 - 9


0.40x = 4.5


x = 4.5/0.40


x = 11.25

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So that means you need to add 11.25 liters of 85% alcohol solution to the initial 30% solution to mix it to get a 45% solution.