I wonder if there is a name or reference for the following fact. It is not the proof I am looking for.

Let $s_1, s_2, ...,s_n$ be non-negative real numbers ordered in a non-increasing way. Let $b_1,b_2,...,b_n$ be non-negative real numbers ordered in a non-decreasing way (so opposite of the $s_i$).

Then the average value $$\frac{s_1+s_2+\cdots +s_n}{n}$$ is at least as large as the weighted average $$\frac{b_1 s_1+\cdots+b_n s_n}{b_1+\cdots+b_n}.$$

Thanks!