Question 879794
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 <font color="red">11.25 liters</font> of 85% alcohol solution to the initial 30% solution to mix it to get a 45% solution.