Question 23
Determine all triples $(x, y, z)$ of positive real numbers that satisfy
$$
\begin{aligned}
3\lfloor x \rfloor - \{y\} + \{z\} &= 20.3 \\
3\lfloor y \rfloor + 5\lfloor z \rfloor - \{x\} &= 15.1 \\
\{y\} + \{z\} &= 0.9.
\end{aligned}
$$
*For a real number $t$, $\lfloor t \rfloor$ denotes the largest integer not greater than $t$, while $\{t\}$ denotes its fractional part, i.e. $\{t\} = t - \lfloor t \rfloor$. For example, if $t = 15.1$, then $\lfloor t \rfloor = 15$ and $\{t\} = 0.1$. (Unione Matematica Italiana)*
$$
\begin{aligned}
3\lfloor x \rfloor - \{y\} + \{z\} &= 20.3 \\
3\lfloor y \rfloor + 5\lfloor z \rfloor - \{x\} &= 15.1 \\
\{y\} + \{z\} &= 0.9.
\end{aligned}
$$
*For a real number $t$, $\lfloor t \rfloor$ denotes the largest integer not greater than $t$, while $\{t\}$ denotes its fractional part, i.e. $\{t\} = t - \lfloor t \rfloor$. For example, if $t = 15.1$, then $\lfloor t \rfloor = 15$ and $\{t\} = 0.1$. (Unione Matematica Italiana)*