Question

aflați numerele x, y, z, tu știind ca sunt invers proporționale cu numerele 1/2 ;1/3 ;0,4 ;0,2 și ca suma lor este 5

Answer 1

x/2=y/3=4z/10=2t/10=k=> x=2k; y=3k; z=10k/4=5k/2 sit=10k/2=5k suma x+y+z+t=5=> 2k+3k+5k/2+5k=5. Eliminam numitorul => 4k+6k+5k+10k=10=> 25k=10 =>k=10/25 => k=0,4 =>x=0,8; y=1,2;;;z=1 si t=2

Answer 2

[tex]\{x,y,z,t\} ip \{\frac{1}{2},\frac{1}{3},0,4,0,2\}\Rightarrow \frac{\frac{x}{1}}{\frac{1}{2}}=\frac{\frac{y}{1}}{\frac{1}{3}}=\frac{\frac{z}{1}}{\frac{4}{10}}=\frac{\frac{t}{1}}{\frac{2}{10}}\Rightarrow\\ \Rightarrow \frac{x}{2}=\frac{y}{3}=\frac{2z}{5}=\frac{t}{5}=k\Rightarrow x=2k,y=3k,z=\frac{5k}{2},t=5k\\ x+y+z+t=5\\ 2k+3k+\frac{5k}{2}+5k=5\\ 10k+\frac{5k}{2}=5|\cdot 2\\ 20k+5k=10\\ 25k=10\Rightarrow k=\frac{10}{25}=0,4\\ Si\ de\ aici\ inlocuiesti\ si\ afli\ fiecare\ numar.....[/tex]