Question 865059
Let's say this solution is a mixture of water and alcohol. 



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 {{{(2.7 + 0.10x)/(10+x)}}} 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



{{{(2.7 + 0.10x)/(10+x)=0.15}}}



{{{2.7 + 0.10x=0.15(10+x)}}}



{{{2.7 + 0.10x=0.15(10)+0.15(x)}}}



{{{2.7 + 0.10x=1.5+0.15x}}}



{{{2.7 + 0.10x-0.15x=1.5}}}



{{{0.10x-0.15x=1.5-2.7}}}



{{{-0.05x=-1.2}}}



{{{x=-1.2/(-0.05)}}}



{{{x=24}}}



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 <font size=4 color="red">24 liters</font> of the 10% alcohol solution with 10 liters of the 27% alcohol solution to get a final solution of 15% alcohol.



Final Answer:  <font size=4 color="red">24 liters</font>