PDA with an unusual double inequality I have an odd PDA problem that I cant seem to construct. I haven't come across one like this before. 

$L = \{w\in\{a,b\}^{*} : 3\#_{a}(w) \leq 5\#_{b}(w) \leq 4\#_{a}(w)\}$

Could I get some pointers on how to tackle such a problem like this so I can be more familiar with the approaches here.
It's your exercise, so you should solve it yourself... but I will give you two hints.


Study the methods used in Grammar for a language with 1/3 of a&#39;s.  They are helpful.
Use non-determinism.  Build a non-deterministic PDA.  (How do you think non-determinism might help here?)