Question

Suma a trei numere este 62 .Aflati numerele stiind ca sunt invers proportionale cu 6,9 si 15 .

Answer 1

a+b+c=62  (1)
a·6=b·9=c·15=k  ⇒ a=k/6,b=k/9,c=k/15  si inlocuind in (1) avem :
k/6+k/9+k/15=62⇔ 31k/90=62 I :31 ⇔k/90=2⇔k=180
a=k/6=180/6=30
b=180/9=20
c=180/15=12

Answer 2

$x+y+z=62 \\ x \cdot6=b \cdot 9 =c \cdot15 =k\\ \Rightarrow x= \frac{k}{6} \\ \\ \Rightarrow y= \frac{k}{9} \\\\ \Rightarrow x= \frac{k}{15} \\ \\ \Rightarrow \frac{k}{6} + \frac{k}{9} + \frac{k}{15} =62 \\ \\ \frac{93k}{270} =62 \\ 93k=270 \cdot 62 \\ 93k=16740 \\ k= \frac{16740}{93} \\ \bold{k=180}$
$\\ \Rightarrow x= \frac{180}{6} \\ \Rightarrow \boxed{x=30}; \\ y= \frac{180}{9} \\ \Rightarrow \boxed{y=20}; \\ z= \frac{180}{15} \\ \Rightarrow \boxed{z=12}. \\ \\ \bold{Verificare:} x+y+z=30+20+12=50+12=\boxed{62}. \ (Adevarat)$