Example 6: On a page of a cloth store's ledger, ink has stained the page, as shown in the table below:

The number of meters of cloth sold is unclear, but it is remembered that it was sold in whole meters; in the amount column, only the three digits 7.28 are visible, but the first three digits are unclear. Please help to investigate this entry.
(1993, 1st "Jin Qiao Cup" Mathematics Knowledge Application Competition for Middle School Students in Shanghai)
Solution: Let the quantity purchased be $x$ meters, and the first three digits of the amount be $y$. According to the problem, we have
$$
49.36 x=10 y+7.28 \text {. }
$$

Therefore, $y=\frac{617 x-91}{125}$
$$
\begin{aligned}
=5 x-1+ & \frac{2(17-4 x)}{125} . \\
\text { Let } \frac{17-4 x}{125}=t \Rightarrow x & =\frac{17-125 t}{4} \\
& =4-31 t+\frac{1-t}{4} .
\end{aligned}
$$

Let $\frac{1-t}{4}=t_{1} \Rightarrow t=1-4 t_{1}$. Substituting, we get
$$
\left\{\begin{array}{l}
x=125 t_{1}-27, \\
y=617 t_{1}-134 .
\end{array}\right.
$$
$100<y<1000$
$$
\Rightarrow 100<617 t_{1}-134<1000 \text {. }
$$

Therefore, $\frac{234}{617}<t_{1}<\frac{1134}{617}$.
Thus, $t_{1}=1$.
Hence, $x=98, y=483$.
Therefore, the quantity of cloth sold is 98 meters, and the amount is 4837.28 yuan.