Question

Numerele naturale x,y,z sunt direct proportionale cu 0,1 ; 0,2 ; 0,3 iar 3x+2y+5z=110. Aflati x,y,z.

Answer 1

Răspuns:

Explicație pas cu pas:

$\dfrac{x}{0,1} = \dfrac{y}{0,2} = \dfrac{z}{0,3} \iff \dfrac{x}{\dfrac{1}{10}} = \dfrac{y}{\dfrac{2}{10}} = \dfrac{z}{\dfrac{3}{10}} = k$

$x = \dfrac{k}{10} \ ; \ y = \dfrac{2k}{10} \ ; \ z = \dfrac{3k}{10}$

$3 \cdot \dfrac{k}{10} + 2 \cdot \dfrac{2k}{10} + 5 \cdot \dfrac{3k}{10} = 110 \\ \iff \dfrac{3k}{10} + \dfrac{4k}{10} + \dfrac{15k}{10} = 110$

$\dfrac{3k+4k+15k}{10} = 110 \iff 22k = 1100 \implies k = 50$

=>

$x = \dfrac{50}{10} \implies x = 5 \\y = \dfrac{2*50}{10} \implies y = 10 \\z = \dfrac{3*50}{10} \implies z = 15$