$370 \mathrm{~K}$ is to be divided among $A, B$, and $C$ such that $A$ receives as many times more than $B$ as $B$ receives more than $C$. How much does each receive if the share of $B$ and $C$ is $50 \mathrm{~K}$ more than the share of $A$?
$A x \mathrm{~K}-\mathrm{t}, B \quad y$ K-t, and $C z \mathrm{~K}$-t receive. Then

$$
x+y+z=370
$$

and

$$
y+z-x=50
$$

so

$$
\begin{gathered}
2 x=370-50=320, \\
x=160 \mathrm{~K} .
\end{gathered}
$$

Furthermore

$$
\begin{gathered}
\frac{160}{y}=\frac{y}{z}, \\
y^{2}=160 z
\end{gathered}
$$

and

$$
\begin{gathered}
y+z=370-160=210 \\
y^{2}=160(210-y) \\
y^{2}+160 y-33600=0
\end{gathered}
$$

from which

$$
y=120 \mathrm{~K}, \quad \mathrm{~and} \text { thus } \quad z=90 \mathrm{~K}
$$