Question

Aflati x,y,z , stiind ca sunt direct proportionale cu numerele 0,1; 2pe 5; 1pe 3 ; si ca suma lor este 1 .

Answer 1

$\frac{x}{ \frac{1}{10} } = \frac{y}{ \frac{2}{5} } = \frac{z}{ \frac{1}{3} }=k$
$\frac{x}{ \frac{1}{10} }=10x$
$\frac{y}{ \frac{2}{5} }= \frac{5y}{2}$
$\frac{z}{ \frac{1}{3} }=3z$ 
$10x=k \\ x= \frac{k}{10} \\ \\ \frac{5y}{2} =k \\ y= \frac{2k}{5} \\ \\ 3z=k \\ z= \frac{k}{3 }$
$\frac{k}{10}+\frac{2k}{5}+\frac{k}{3} =1 \\ \frac{25k}{30} =1 \\ 25k=30 \\ k=30/25= \frac{6}{5}$
$x= \frac{5}{60} \\ \\ y= \frac{12}{25} \\ \\ z= \frac{6}{15}$