let x = 50% and y = 13%
We need 5 liters of 27.8% acid.
A) x + y = 5
B) .50x + .13y = (.278 * 5)
We multiply A by -.5
A) -.5 x + -.5 y = -2.5 then we add it to B
B) .50x + .13y = (1.39 )
-.37y = -1.11
y = 3
x = 2
So, we need 2 liters of 50% and 3 liters of 13%.