Question 915910
You can solve this question by either the substitution method or the elimination method.  I am going to illustrate the substitution method here.  

   Lets let a= adult ticket and c = children's ticket
   We need two equations for this problem with two unknowns. 

  The first equation would then be 
    3a + 4c = 129

  The second equation would be
    2a + 3c = 92 


Let's solve the first equation for a:

3a + 4c = 129

3a = 129 - 4c

a = 129/3 - 4/3c

a = 43-4/3c

Now we can replace a in the second equation:

2a + 3c = 92

2(43 - 4/3c) + 3c= 92

86 -8/3c +3c =92

subtract 86 and covert to thirds

-8/3c + 9/3c =6

1/3c= 6

multiply *3 

c = 18

Find a by using one of the 2 equations from the beginning

 2a + 3c = 92

2a + 3*18 = 92
2a + 54 = 92
2a = 38
a = 19 

check answer with the other equation.  

 3a + 4c = 129

3*19 + 4*18 =129
57 + 72 =129
129=129