Răspuns :
[tex]\displaystyle\bf\\x;~y;~z~~d.p.~~3;~6;~11\\\\Metoda~1~de~rezolvare:\\\\k=\frac{1000}{3+6+11}=\frac{1000}{20}=50\\\\x=3\times50=150\\y=6\times50=300\\z=11\times50=550\\\\\\Metoda~2~de~rezolvare:\\\\\frac{x}{3}=\frac{y}{6}=\frac{z}{11}=k\\\\x=3k\\y=6k\\z=11k\\\\x+y+z=1000\\3k+6k+11k=1000\\20k=1000\\\\k=\frac{1000}{20}=50\\\\x=3k=3\times50=150\\y=6k=6\times50=300\\z=11k=11\times50=550[/tex]
Notare nr. : a, b, c
(a, b, c) d. p ( 3,6,11)
a/3 = b/6=c/11 = k
a=3k, b=6k, c=11 k
a+b+c= 1000 => 3k+6k+11k = 1000
20 k = 1000 => k=1000 : 20 = 50
a=3 * 50 =>a=150
b=6 * 50 =>b=300
c=11 * 50 =>c=550
Verificare : 150 + 300 + 550 = 450 + 550 = 1000 ☑️
Numerele sunt : 150,300,550