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 ?
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.