Question

determinati numerele rationale pozitive x,y,z,t,care sunt direct proportionale cu 2,3,5,7 iar 7x+9y+3z+2t=350

Answer 1

[tex]\{x,y,z,t\}d.p. \{2,3,5,7\}\Rightarrow \dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=\dfrac{t}{7}=k\Rightarrow x=2k,y=3k, \\ z=5k,t=7k\\ 7x+9y+3z+2t=350 \\ 7\cdot 2k+9\cdot 3k+3\cdot 5k+2\cdot 7k=350\\ 14k+27k+15k+14k=350\\ 70k=350\Rightarrow \boxed{k=5}\\ x=2k\Rightarrow \boxed{x=10}\\ y=3k\Rightarrow \boxed{y=30}\\ z=5k\Rightarrow \boxed{z=15}\\ t=7k\Rightarrow \boxed{t=35}[/tex]