Answer: the price of a senior citizen's ticket is $8.
the price of a child's ticket is $14
Explanation:
Let x represent the price of a senior citizen's ticket.
Let y represent the price of a child's ticket.
On the first day of ticket sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. It means that
3x + y = 38- - - - - - - - - - - -1
The school took in $52 on the second day by selling 3 senior citizen and 2 child tickets. It means that
3x + 2y = 52- - - - - - - - - - - -2
Subtracting equation 2 from equation 1, it becomes
- y = - 14
y = 14
Substituting y = 14 into equation 1, it becomes
3x + 14 = 38
3x = 38 - 14 = 24
x = 24/3
x = 8