Question

Sa se imparta numarul 38 in parti invers proportionale cu numerele 2/3 , 1/6 , 1/2
Simbol: / = linie de fractie

Answer 1

{ a, b, c } i.p. { 2/3, 1/6, 1/2 }
a x 2/3 = b x 1/6 = c x 1/2 = k
a x 2/3 = k ⇒ a = 3k/2
b x 1/6 = k ⇒ b = 6k
c x 1/2 = k ⇒ c = 2k
        2)      2)
3k/2 + 6k + 2k = 38
3k/2 + 12k/2 + 4k/2 = 38
19k/2 = 38
19k = 38 x 2
19k = 76
k = 76 : 19
k = 4
a = 3 x 4 / 2 = 12/2 = 6
b = 6 x 4 = 24
c = 2 x 4 = 8

Answer 2

               
$x+y+z=38 \\ x* \frac{2}{3}=y* \frac{1}{6}=z* \frac{1}{2} = k \\ =>x = \frac{3k}{2} \;\;\;si\;\;\;y=6k \;\;\;si\;\;\;z=2k \\ x+y+z = \frac{3k}{2}+6k +2k=38 \\ \frac{3k}{2}+ \frac{12k}{2}+ \frac{4k}{2}=38 \\ \frac{3k+12k+4k}{2}=38 \\ \frac{19k}{2}=38 \\ 19k=2*38 \\ k= \frac{2*38}{19}=2*2=4 \\ \\ x = \frac{3k}{2}=\frac{3*4}{2}=12/2=\boxed{6} \\ y=6k=6*4=\boxed{24} \\ z=2k=2*4=\boxed{8}$