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There were 3/5 as many children as adults on a bus. At the next stop, 3 children boarded and 2 adults alighted from the bus. Then, there were 5/6 as many children as adults on the bus. How many children were there on the bus at first ?

 Sep 2, 2021
 #1
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First steps for solving a problem like this generally involves a system of equations.

We want to get the values from the initial frame of reference, so let's use that as the starting point

 

c = # children

a = # adults

 

3c = 5a

 

Then at the stop, we find another fraction after some changes

 

5(c+3) = 6(a-2)

 

Now let's expand it.

 

5c + 15 = 6a - 12
5c = 6a - 27

Now let's rewrite the initial relationship to get it in terms of a.

 

a = 3/5 c

 

And substitute it in...

 

5c = 6(3/5 c) - 27
5c = 18/5 c - 27

 

We can multiply the entire equation by 5 to remove that pesky fraction

 

15c = 18c - 135

-3c = -135

c = 45

 

Thus there were 45 children on the bus at first.

 Sep 2, 2021

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