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 ?

florianmanteyw Sep 2, 2021

#1**-1 **

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.

helperid1839321 Sep 2, 2021