SOLUTION: In a zoo, the ratio of adults to children is 3 to 9. If there are 96 people in the zoo, how many children are there?

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Question 1156483: In a zoo, the ratio of adults to children is 3 to 9. If there are 96 people in the zoo, how many children are there?

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
Answer by ikleyn(52784) About Me  (Show Source):
You can put this solution on YOUR website!
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            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  96%2F12 = 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

    adults%2Fchildren = %2896-x%29%2Fx = 3%2F9 = 1%2F3.


Again

    %2896-x%29%2Fx = 1%2F3.


From this proportion,

    3*(96-x) = x.


Simplify and solve for x

    3*96 - 3x = x

    3*96 = x + 3x = 4x

    x = %283%2A96%29%2F4 = 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).