Help!

This problem single handedly screwed my quant section this week. I can't remember the exact numbers involved, but it was something like:

'n' parents split the $300 cost of a school trip equally. If the school had three less parents, each the parents would each pay an additional $3. Find 'n'

my method was...
300/n = x
300 = nx

and

300/n-3 = x +3
300 = nx + 3n - 3x - 9
sub nx = 300
300 = 300 + 3n - 3x - 9
9 = 3(n - x)
3 = n - x
.... then I don't know, not sure if I'm even doing this right. I think it was just jitters, but i spent 5 full minutes on this and finally just guessed.

My question is: what's the correct method here and has anyone seen a question similar to this so I can work it out with numbers that actually add up? This seems really easy but I'm just not getting something and it's driving me insane. Thanks!