Problem 9.3. The teacher wrote an arithmetic example on the board: the product of two mixed fractions equals 43. Then he replaced the denominator of the first fraction with $X$, and the integer part of the second fraction with $Y$. The resulting expression is

$$
5 \frac{1}{X} \cdot Y \frac{1}{2}=43
$$

Restore the example.
Answer: $X=17, Y=8$.

Solution. Since $5\frac{43}{5}>Y \frac{1}{2} \geqslant \frac{43}{5.5}=\frac{86}{11}>7.5
$

The number $Y$ is an integer, so $Y=8$.

Then $5 \frac{1}{X}=\frac{43}{8.5}=\frac{86}{17}=5 \frac{1}{17}$, so $X=17$.