Question

Calculati numerele x,y,z stiind ca x supra 2=y supra 3= z supra 5 si 2x+ y+3z=44
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Answer 1

 

$\displaystyle\bf\\\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=k\\\\x=2k\\y=3k\\z=5k\\\\2x+ y+3z=44\\\\2\cdot2k+3k+3\cdot5k=44\\\\4k+3k+15k=44\\\\22k=44\\\\k=\frac{44}{22}\\\\\boxed{\bf~k=2}\\\\x=2k=2\cdot2=4\\y=3k=3\cdot2=6\\z=5k=5\cdot2=10\\\\\boxed{\begin{cases}\bf~x=4\\\bf~y=6\\\bf~z=10\end{cases}}$