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Word Problem

A solution is 10% citric acid. if 3 liters of a 20% citric acid solution are added to it, the result is a solution this is in a ratio of 13 parts citric acid to 102 parts "other than citric acid". How many total liters were in the original solution (before 3 L were added)?
 
 
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1 Answer

x = liters of original 10% citric acid.
 
3(20%) + x(10%) = liters citric acid
 
3 + x = total liters
 
(3(20%) + x(10%)) / (3 + x) = 13 / (102 + 13)
 
13(3 + x) = 115(3(20%) + x(10%))
 
39 + 13x = 115(3/5 + x/10)
 
39 + 13x = 23(3) + 11.5x
 
1.5x = 30
 
x = 300/15
 
x = 20 liters