I have two cans of paint. can a has 9 parts of blue paint to one part of yellow paint. can b is 20 percent blue paint and the rest is yellow paint. how much paint should i use from each can to obtain 8 liters of paint which is half blue and half yellow.

Can A is ---------- > 9 parts of blue  1 part yellow= 90% blue, 10% yellow
Can B is 20% blue, 80% yellow. 
let
A + B = 8 Liters 

90% A + 20% B = 50% (Blue) 
10% A + 80% B = 50% (Yellow) 

resolving 

90% A + 20% B = 10% A + 80% B 
80% A = 60% B 

Go back to A + B = 8 and solve for one of the variables. 
B = 8 - A 

80% A = 60% (8 - A) 
80% A = 480% - 60% A 
140% A = 480% 
A = 3 43 liters

B = 8 - A = 4.57 liters

The answer is 3.43 liters of Can A, and 4.57 liters of Can B.