how can an equation involving ceilings be solved? (c is a known constant, looking for n)?:
$$c=n-60\left \lceil \frac{n}{650} \right \rceil-70\left \lceil \frac{n}{600} \right \rceil-25\left \lceil \frac{n}{800} \right \rceil$$
A solution for $c=10000$ would be $n=13295$
I don't know how to deal with the ceilings. I thought about case distinction but it doesn't make sense. If you think of Max and Min values of the ceilings then you get 3 inequalities but I don't know how to fuse them.