Question

Determinati numerele x ,y , z stiind ca sunt direct proportionale cu 2 , 5 , 7 si x + 5y + 7z = 760

Answer 1

x/2=y/5=z/7=k
x/2=k⇒x=2k
y/5=k⇒y=5k
z/7=k⇒z=7k
Inlocuim in x+5y+7z=760 si obtinem:
2k+5×5k+7×7k=760
2k+25k+49k=760
76k=760⇒k=760:76
               k=10⇒x=20
                          y=50
                          z=70

Answer 2

[tex](x,y,z)\sim(2,5,7)\Rightarrow \frac{x}{2}=\frac{y}{5}=\frac{z}{7}=k\\ \Rightarrow x=2k,\y=5k,\ z=7k\\ x+5y+7z=2k+5\cdot 5k+7\cdot 7k=2k+25k+49k=760 \Rightarrow\\ 76k=760 \Rightarrow k=10\\ x=2k=20\\ y=5k=50\\ z=7k=70[/tex]