we can make an equation for this (x is the number of children)
[tex]x + (x + 109) = 243 \\ 2x + 149 = 243 \\ 2x = 243 - 149 = 134 [/tex]
[tex]x = \frac{134}{2} = 67[/tex]
there are 67 children in the theater
67+ 109=176
and there are 176 adults.
good luck