310. Three men trade a horse for 12 florins, but none of them individually has that amount. The first says to the other two: "Give me half of your money each, and I will buy the horse." The second says to the first and the third: "Give me one third of your money each, and I will acquire the horse." Finally, the third says to the first two: "Give me only one quarter of your money each, and the horse will be mine." Now the question is, how much money did each have?
310. Let the 1st have $x$, the 2nd have $y$, the 3rd have $z$.

Then

$$
\begin{aligned}
& x+\frac{1}{2}(y+z)=12 \\
& y+\frac{1}{3}(x+z)=12 \\
& z+\frac{1}{4}(x+y)=12
\end{aligned}
$$[^0]

Solving the system is not difficult:

$$
x=3 \frac{9}{17} ; y=7 \frac{13}{17} ; z=9 \frac{3}{17}
$$