[tex]a) \: \frac{x}{6} = \frac{y}{7} = \frac{z}{8} [/tex]
[tex]x = \frac{6y}{7} [/tex]
[tex]z = \frac{8y}{7} [/tex]
[tex] \frac{6y}{7} + y - \frac{8y}{7} =20 [/tex]
[tex] = > 6y + 7y - 8y = 140[/tex]
[tex] => 5y = 140 \\ y = \frac{140}{5} \\ y = 28 \\ x = 24 \\ z = 32[/tex]
[tex]b) x = \frac{5y}{3} \\ z = \frac{7y}{3} \\ \frac{5y}{3} +2y - \frac{7y}{3} = 192 \\ = > 5y + 6y - 7y = 576 \\ => 4y = 576 \\ y = 144 \\ x = 240 \\ z = 336[/tex]
[tex]c) x = \frac{14y}{11} \\ z = \frac{12y}{11} \\ \frac{14y}{11} +y - \frac{12y}{11} = 429 \\ = > 14y + 11y - 12y = 429 \\ => 13y = 429 \\ y = 33 \\ x = 42 \\ z = 26[/tex]
