Let x = the volume of the 15% acid (in liters) and 

let y = the volume of the 30% acid.


Then the volume of the 75% acid is 2y liters.


Then your equations are

    x +    y +       2y = 216,         (1)     (total volume)
0.15x + 0.3y + 0.75*(2y) = 0.25*216    (2)    (pure acid volume)


Simplify:

    x +   3y = 216,                    (3)
0.15x + 1.8y =  54.                    (4)


Simplify one more time by multiplying eq(4) by 100 (both sides)

    x +   3y =  216,                   (5)
  15x + 180y = 5400.                   (6)


Now multiply eq(5) by 15 (both sides). The modified system is

  15x +  45y = 3240,                   (7)
  15x + 180y = 5400.                   (8)


Next subtract eq(7) from eq(8).  The terms "15x" will cancel each other, 
and you will get a single equation for only one unknown "y".    (It is how the Elimination method works).

  180y - 45y = 5400 - 3240,

  135y = 2160  ====>  y =  = 16.


Answer.  16 liters of the 30% solution,  16*2 = 32 of the 75% solution and the rest 216-(16+32) = 168 liters of the 15% solution.


Check.  0.3*16 + 0.75*32 + 0.15*168 = 54 liters of pure acid;

        0.25*216 = 54 liters of pure acid.   ! Correct !