Question 1156483
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            I will show you three ways to solve the problem.



1. &nbsp;&nbsp;<U>MENTAL solution</U>


<pre>
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  {{{96/12}}} = 8.

From it, you easily conclude that the number of children is  9*8 = 72.    <U>ANSWER</U>
</pre>

Solved.



2.  &nbsp;&nbsp;<U>ALGEBRA solution for beginners</U> &nbsp;&nbsp;(5-th grade)


<pre>
Let x be the number of children.

Then the number of adults is 96-x.


Then you write this proportion, based on the condition

    {{{adults/children}}} = {{{(96-x)/x}}} = {{{3/9}}} = {{{1/3}}}.


Again

    {{{(96-x)/x}}} = {{{1/3}}}.


From this proportion,

    3*(96-x) = x.


Simplify and solve for x

    3*96 - 3x = x

    3*96 = x + 3x = 4x

    x = {{{(3*96)/4}}} = 3*24 = 72.     <U>ANSWER</U>  (the same as above)
</pre>

Solved.



3.  &nbsp;&nbsp;<U>ALGEBRA solution for more advanced students</U> &nbsp;&nbsp;(6-th grade and higher, until &nbsp;90 &nbsp;years old)


<pre>
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.
</pre>

Solved &nbsp;(3 times by &nbsp;3 methods, &nbsp;in order for provide you the best knowledge).