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. $\newline$ How many children are at the movie? $\newline$ $\square$ children

Full solution

Q. 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.

\newline

How many children are at the movie?

\newline

\square

children

Ratio Calculation: For every $9$ children, there are $4$ adults. So the ratio of children to adults is $9:4$ .
Assign Variables: Let's call the number of groups of children and adults $x$ . This means there are $9x$ children and $4x$ adults.
Total Number Calculation: The total number of children and adults is $39$ . So, $9x + 4x = 39$ .
Combine Like Terms: Combine like terms: $13x = 39$ .
Solve for x: Divide both sides by $13$ to find x: $x = \frac{39}{13}$ .
Calculate x: Calculate $x$ : $x = 3$ .
Calculate Number of Groups: Now, we know there are $3$ groups of children. Multiply the number of groups by the number of children in each group: $9$ children/group $*$ $3$ groups.
Calculate Number of Children: Calculate the number of children: $9 \times 3 = 27$ children.