Question

determinati numerele x,y,z direct proportionale cu numerele 2,3 si 4 stind ca. x+y+z= 45 ​

Answer 1

Răspuns:

x+y+z = 45

2k+3k +4k = 45

5k+4k=45

9k = 45

k= 45:9

k = 5

x= 2×5=10

y= 3×5=15

z= 4×5=20

Answer 2

$\it x+y+z=45\ \ \ \ \ (*) \\ \\ \{x,\ y,\ z\}\ d.\ p.\ \{2,\ 3,\ 4\} \Rightarrow \dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{4}=\dfrac{x+y+z}{2+3+4}\ \stackrel{(*)}{=}\ \dfrac{45}{9}=5\\ \\ \\ \dfrac{x}{2}=5 \Rightarrow x=2\cdot5=10\\ \\ \\ \dfrac{y}{3}=5 \Rightarrow y=3\cdot5=15\\ \\ \\ \dfrac{z}{4}=5 \Rightarrow z=4\cdot5=20$