Question 6
Suppose $r$ is a real number for which $$
\begin{aligned}&\left\lfloor r+\frac{19}{100}\right\rfloor+\left\lfloor r+\frac{20}{100}\right\rfloor\\&\quad+\left\lfloor r+\frac{21}{100}\right\rfloor+\cdots\\&\quad+\left\lfloor r+\frac{91}{100}\right\rfloor=546.\end{aligned}
$$ Find $\lfloor100r\rfloor.$ (For real $x,$ $\lfloor x\rfloor$ is the greatest integer less than or equal to $x.$)
\begin{aligned}&\left\lfloor r+\frac{19}{100}\right\rfloor+\left\lfloor r+\frac{20}{100}\right\rfloor\\&\quad+\left\lfloor r+\frac{21}{100}\right\rfloor+\cdots\\&\quad+\left\lfloor r+\frac{91}{100}\right\rfloor=546.\end{aligned}
$$ Find $\lfloor100r\rfloor.$ (For real $x,$ $\lfloor x\rfloor$ is the greatest integer less than or equal to $x.$)