Start by writing out the information you know mathematically (I used S for cost of senior ticket, and C for cost of child ticket. You could use X and Y, or any other combination of letters as variables)
3s + 1c=38
3s + 2c=52
Now, you'll want to eliminate one of the variables by subtracting it out. Remember - Same sign, subtract (and therefore different sign, add).
In this case, 3s exists in the first and second equation, so it's very easy to get rid of. They're both positive, so they have the same sign (+). Same sign, subtract.
3s + 1c=38
-(3s + 2c=52)
__________
0 -1c= -14
-c=-14
C=14
Now, plug c=14 into either of the original equations.
3s + C= 38
3s + 14=38
3s=24
S=8.
So, a child ticket costs $14 and a senior ticket costs $8.
