8:17 AM
Personally I think the the tags (density) and (linear), which you have created in this question should be removed altogether. The tags with ambiguous names which are used in various contexts are very probably going to be misused. But if you really see the need for creating these new tags, the very least you should do is describing the intended usage in the tag-excerpt and tag-wiki.
2

Let $r_1, \ldots, r_n$ be a set of positive reals. Define $S = \{a_1r_1+\cdots+a_nr_n : a_i\in \mathbb{N}\}$. Define $\pi(x)= |\{a\in S:a<x\}|$. Is there an asymptotic formula for $\pi(x)$ as $x \to \infty$ ? For $n=1$, $\pi(x) \approx x/a_1$. But I'm pretty unsure how to generalize this.