From the condition, you have these 2 equations


      x +   y =   55  dollars     (1)

    20x + 25y = 1175  dollars     (2)


whose meaning is clear without any explanations.


From equation (1), express  x = 55-y  and substitute it into equation (2). You will get


    20*(55-y) + 25y = 1175

    1100 - 20y + 25y = 1175

    5y               = 1175 - 1100 = 75

     y                             = 75/5 = 15.


Then from equation (1),  x = 55 - 15 = 40.


ANSWER.  40 advance and 15 same day tickets.


Check.   20*40 + 15*25 = 1175 dollars.    ! Correct !