At the newest animated movie, for every
\[9\] children, there are
\[4\] adults. There are a total of
\[39\] children and adults at the movie.
How many children are at the movie?
Let's assume the number of children is $x$. According to the given information, we can form the equation $\frac{x}{9}=\frac{39-x}{4}.$
Multiplying both sides of the equation by $9\cdot4=36$ gives $4x=36(39-x).$
Expanding the right side gives $4x=36\cdot39-36x.$
Combining like terms gives $4x=1404-36x.$
Adding $36x$ to both sides gives $40x=1404.$
Finally, dividing both sides by $40$ gives $x=\boxed{35},$ which is the number of children at the movie.