I've been going through lots of my math textbooks, and I'm able to solve a lot of them using some specific method or formula. But there's one problem I've come across quite a few times that I just couldn't figure out how to do. One example is...
Suppose that $\frac {4}{2001} < \frac {a}{a+b} < \frac {5}{2001}$. Compute the number of different possible integer values that $\frac {b}{a}$ can take on.
Does anyone know a reliable method to do these kind of these problems, or even better, a formula? My best attempts have been to manually list out all of the possibilities, and it would really help if someone could explain a good way to do these kind of problems.
Hint: the inequality you are trying to satisfy is the same as $$\frac{2001}{4} > \frac{a+b}{a} > \frac{2001}{5}.$$