Example 1 (9th American Invitational Mathematics Examination AIME Problem) Let $r$ be a real number satisfying the condition:
$$
\left[r+\frac{19}{100}\right]+\left[r+\frac{20}{100}\right]+\left[r+\frac{21}{100}\right]+\cdots+\left[r+\frac{91}{100}\right]=546 \text {. }
$$

Find $[100 r]$.