Answer:
Step-by-step explanation:
Letting "a" and "c" represent the costs of adult tickets and child tickets, the problem statement gives us two relations:
 3a +5c = 52
 2a +4c = 38
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We can solve this system of equations using "elimination" as follows:
Dividing the first equation by 2 we get
 a +2c = 19
Multiplying this by 3 and subtracting the first equation eliminates the "a" variable and tells us the price of a child ticket:
 3(a +2c) -(3a +4c) = 3(19) -(52)
 c = 5 . . . . . . collect terms
 a +2·5 = 19 . . substitute for c in the 3rd equation above
 a = 9 . . . . . . subtract 10
One adult ticket costs $9; one child ticket costs $5.
