.
I will show you three ways to solve the problem.
1. MENTAL solution
The condition means that you can group all the people in groups in a way that each group contains 3 adults and 9 children.
Each such a group contains 3+9 = 12 persons.
Therefore, the number of such groups is = 8.
From it, you easily conclude that the number of children is 9*8 = 72. ANSWER
Solved.
2. ALGEBRA solution for beginners (5-th grade)
Let x be the number of children.
Then the number of adults is 96-x.
Then you write this proportion, based on the condition
= = = .
Again
= .
From this proportion,
3*(96-x) = x.
Simplify and solve for x
3*96 - 3x = x
3*96 = x + 3x = 4x
x = = 3*24 = 72. ANSWER (the same as above)
Solved.
3. ALGEBRA solution for more advanced students (6-th grade and higher, until 90 years old)
Notice that the ratio 3:9 is the same as 1:3.
Let x be the number of adults.
Then the number of children is 3x, according to the condition.
From the condition, you have
x + 3x = 96,
4x = 96,
x = 96/4 = 24.
Hence, the number of children is 3*24 = 72.
Solved (3 times by 3 methods, in order for provide you the best knowledge).