**25 of 16oz cups**

12oz cup - x,

16oz cup - y,

20oz cup -z

x+y+z=55 --------------> (1)

12x+16y+20z=6*144 => 3x+4y+5z=216 --------------> (2)

1.4x+1.6y+1.7z=85.90 => 14x+16y+17z=859 --------------> (3)

(3)- 14*(1) => 2y+3z=89 --------------> (4)

(2) - 3*(1) => y+2z=51 --------------> (5)

2*(5) - (4) => **z=13**, then using (5) and (1) we find **y=25 and x=17**