A circular disc is composed of 4 equal weight circular segments. The first segment is copper (density 8.7), the second is silver (10.5), the third is gold (19.2), and the fourth is platinum (21). What is the central angle corresponding to each of the circular segments?
Ha az egymásután következő körczikkek középponti szögei $x, y, z, u$; akkor

$$
8.7 x=10.5 y=19.2 z=21 u
$$

és

$$
x+y+z+u=360
$$

A megoldandó egyenlet tehát:

$$
x+\frac{8.7}{10.5} x+\frac{8.7}{19.2} x+\frac{8.7}{21} x=360
$$

miből

$$
x=133^{\circ} 31^{\prime} 55^{\prime \prime}
$$

továbbá

$$
y=110^{\circ} 38^{\prime} 27^{\prime \prime}, z=60^{\circ} 30^{\prime} 25^{\prime \prime} \text { és } u=55^{\circ} 19^{\prime} 13^{\prime \prime}
$$

(Jánosy Gyula, Budapest.)

A feladatot még megoldották: Bánó L., Ehrenstein P., Freund E., Harsányi Z., Jánossy F., Kiss J., Schlesinger Gy., Schwarz O. - A budapesti ág. h. ev. főgymn. V. osztálya.

If the central angles of the consecutive arcs are $x, y, z, u$; then

$$
8.7 x=10.5 y=19.2 z=21 u
$$

and

$$
x+y+z+u=360
$$

The equation to solve is therefore:

$$
x+\frac{8.7}{10.5} x+\frac{8.7}{19.2} x+\frac{8.7}{21} x=360
$$

from which

$$
x=133^{\circ} 31^{\prime} 55^{\prime \prime}
$$

furthermore

$$
y=110^{\circ} 38^{\prime} 27^{\prime \prime}, z=60^{\circ} 30^{\prime} 25^{\prime \prime} \text { and } u=55^{\circ} 19^{\prime} 13^{\prime \prime}
$$

(Jánosy Gyula, Budapest.)

The problem was also solved by: Bánó L., Ehrenstein P., Freund E., Harsányi Z., Jánossy F., Kiss J., Schlesinger Gy., Schwarz O. - The 5th grade of the Budapest branch of the Royal Gymnasium.