Let x = mass of coffee A, in kilograms.

let y = mass of coffee A, in kilograms.


Then your basic equation is


    190x + 150y = 


or, which is the same


    190x + 150y = 160*(x+y).      (1)


You want to find the ratio  .  To get it, divide equation (1) by "y". You will get


     + 150 = .     (2)


Introduce new variable t = ; then your equation (2) takes the form


    190t + 150 = 160t + 160.


Simplify and solve for "t"


    190t - 160t = 160 - 150

    30t         = 10

      t         =  = .


ANSWER.  The ratio A:B =  = .