Final answer:
To find the number of children who went to the park, we can set up a system of equations using the cost and number of adults and children. Using the method of elimination, we find that there were 5 adults and 14 children.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's use 'a' to represent the number of adults and 'c' to represent the number of children. We can then write two equations based on the given information.
The first equation is: 8a + 5c = 110, which represents the total cost of the tickets.
The second equation is: a + c = 19, which represents the total number of people who went to the park.
To solve this system of equations, we can use substitution or elimination. Let's use elimination here. Multiply both sides of the second equation by 5 to get 5a + 5c = 95. Subtract this equation from the first equation to eliminate 'c'.
8a + 5c - (5a + 5c) = 110 - 95
3a = 15
a = 5
Now that we know there were 5 adults, we can substitute this value back into the second equation to find the number of children.
5 + c = 19
c = 14
Therefore, there were 14 children who went to the park.