Alright this is gonna be a long one
Lets called child tickets x and adult tickets y
so x + y should be equal to 159 since they said that the total sum of the tickets is 159
so thats your first equation : x + y = 159
next form an equation using the prices,
5.40x + 8.70y = 1079.70
now that you have your two equations, just substitute the first into the second (you could either substitute for x or y by saying x = 159-y or that y=159-x)
Hope this helps.