  In a recent work, the present author developed an efficient method to find
the number of solutions of $ax+by+cz=n$ in non-negative integer triples
$(x,y,z)$ where $a,b,c$ and $n$ are given natural numbers. In this note, we use
that formula to obtain some simple looking bounds for the number of solutions
of $ax+by+cz=n$. Using these bounds, we solve some special cases of a problem
related to the generalization of Frobenius coin problem in three variables.
Moreover, we use these bounds to disprove a recent conjecture of He, Shiue and
Venkat regarding the solution structure of $ax+by+cz=n$.
