Question

Determinati numerele x,y si z daca x+y+z=42 si x/5=y/6; y/3=z/5.

Answer 1

$\frac{x}{5} = \frac{y}{6} = k\implies \: \underline{x = 5k} \: , \: \underline{y = 6k} \\ \frac{y}{3} = \frac{z}{5} = t\implies \: y = 3t \: , \: z = 5t \\\small \iff \: 3t = 6k\implies t = 2k\implies \underline{z = 10k} \\\sout{ - - - - - - - - - - - - - - - - } \\\small x + y + z = 42\iff 5k + 6k + 10k = 42 \\\iff 21k = 42\iff \: k = 2 \\ \\ \implies \: x = 5k\implies \: x = 10 \\ \implies \: y = 6k\implies \: y = 12 \\ \implies \: z = 10k\implies \: z = 20$