Răspuns:
[tex]0.(3) = \frac{3}{9} = \frac{1}{3} \\ 0.(6) = \frac{6}{9} = \frac{2}{3} \\ 0.(7) = \frac{7}{9} [/tex]
[tex] \frac{x}{ \frac{1}{3} } = 3x \\ \frac{y}{ \frac{2}{3} } = \frac{3y}{2} \\ \frac{z}{ \frac{7}{9} } = \frac{9z}{7} [/tex]
[tex]3x = \frac{3y}{2} = \frac{9z}{7} = k \\ x = \frac{k}{3} \\ y = \frac{2k}{3} \\ z = \frac{7k}{9} [/tex]
[tex] \frac{5k}{3} + \frac{4k}{3} - \frac{7k}{3} = 18 \\ 2k = 54 \\ k = 27[/tex]
[tex]x = \frac{27}{3} = 9 \\ y = \frac{2 \times 27}{3} = 18 \\ z = \frac{7 \times 27}{9} = 21[/tex]
