Question

Determinati x, y, z dacax+ y + z+ = 135 si x/3 = y/7 = z/5

Answer 1

[tex]\frac{x}{3}=\frac{y}{7}=\frac{z}{5}=\frac{x+y+z}{3+7+5}=\frac{135}{15}=9\\
\\ x=3\cdot 9=27\\
\\ y=7\cdot 9=63\\
\\ z=5\cdot 9=45\\
\\ Sau,~daca~nu~stii~asa:\\
\\ \frac{x}{3}=\frac{y}{7}=\frac{z}{5}=k\\
\\ \Rightarrow x=3k,~y=7k,~z=5k\\
\\ x+y+z=135\\
\\ 3k+7k+5k=135\\
\\ 15k=135\\
\\ k=135:15 \Rightarrow k=9\\
\\ \Rightarrow x=9\cdot 3=27\\
\\ \Rightarrow y=9\cdot 7=63\\
\\ \Rightarrow z=9\cdot 5=45[/tex]