Question

impartiti numarul 120 in parti direct proportionale cu 2,6 si 7

Answer 1

[tex] \frac{x}{2} = \frac{y}{6} = \frac{z}{7} =K \\ x=2k \\ y=6k \\ z=7k \\ 2k+6k+7k=120 \\ k*(2+6+7)=120 \\ k*15=120 \\ k= \frac{120}{15} \\ k=8 \\ \\ x:8=2 \\ x=2*8 \\ x=16 \\ \\ y:8=6 \\ y=6*8 \\ y=48 \\ \\ z:8=7 \\ z=7*8 \\ z=56 \\ \\ V=16+48+56=120[/tex]

Answer 2

Fie x, y, z cele trei părți.

[tex]\it x+y+z = 120\ \ \ \ (*) \\\;\\ \dfrac{x}{2} =\dfrac{y}{6} =\dfrac{z}{7} =\dfrac{x+y+z}{2+6+7} \stackrel{(*)}{=} \dfrac{120}{15} =8[/tex]

x/2 = 8 ⇒ x = 2·8 = 16

y/6 = 8 ⇒ y = 6·8 = 48

z/7 = 8 ⇒ z = 7·8 = 56