Question

Aflati numerele x,y,z stiind ca sunt direct proporționale cu 3,4,5 si 2x-y+3z=102

Answer 1

Răspuns

Explicație pas cu pas:

$\{x,y,z\}~direct~proportional~\{3,4,5\}\Rightarrow \dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}=k\Rightarrow x=3k,y=4k,\\z=5k\\2x-y+3z=102\\2\cdot 3k-4k+3\cdot 5k=102\\6k-4k+15k=102\\17k=102|:17\\\bold{k=6}\\x=3k\Rightarrow \bold{x=18}\\y=4k\Rightarrow \bold{y=24}\\z=5k\Rightarrow \bold{z=30}$

Answer 2

Răspuns

x = 18 ; y = 24 ; z = 30

Explicație pas cu pas:

{ x , y , z } d.p { 3 , 4 , 5 }

2x - y + 3z = 102

------------------------------------

x / 3 = y / 4 = z / 5 = K

x / 3 = K => x = 3 K

y / 4 = K => y = 4 K

z / 5 = K => z = 5 K

2 · 3 K - 4 K + 3 · 5 K = 102

6 K - 4 K + 15 K = 102

2 K + 15 K = 102

17 K = 102

K = 102 : 17

K = 6

x = 6 · 3 = 18

y = 6 · 4 = 24

z = 6 · 5 = 30