SOLUTION: Pure acid is to be added to a 10% solution to obtain 27 liters of a 20% acid solution. What amounts of each should be used? What is my x and y and how do I come up with 2 syst

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Question 788611: Pure acid is to be added to a 10% solution to obtain 27 liters of a 20% acid solution. What amounts of each should be used?

What is my x and y and how do I come up with 2 system of equations?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= amount of acid added (in liters)
y= amount of 10% solution you start with (in liters)

One equation is the balancing of total amounts (in liters)
x%2By=27

The other equation is the balancing of the amount of pure acid:
0.1y%2Bx=0.2%2A27<-->0.1y%2Bx=5.4<-->10x%2By=54
Since you start with y liters of 10% acid, you are starting with 10% of y liters of pure acid in that solution, or
0.1y
You add x liters of pure acid, and end up with 27 liters of a 20% acid solution that must contain 20% of 27 liters of pure acid, or
0.2%2A27

Your system could be
system%28x%2By=27%2Cx%2B0.1y=5.4%29 or system%28x%2By=27%2C10x%2By=54%29

NOTE:
As a chemist, I find this kind of problem offensively wrong in more ways than I care to count, but since I can't beat them, I may as well join them and pretend that it makes sense.