Question

Aflatii a.b.c stind ca sunt proportionale cu 0.5 ; 0.2 ; 0.(3) si a+b+c = 930

Answer 1

$\hbox{ |a, b, c| D.P |0,5; 0,2; 0,(3) | }$⇒ $\frac{a}{ \frac{5}{10} }= \frac{b}{ \frac{2}{10} }= \frac{c}{ \frac{3}{9} }$

$a\cdot \frac{10}{5}=b\cdot \frac{10}{2}=c\cdot \frac{9}{3}$ ⇒ $2a=5b=3c=k$ ⇒  $a= \frac{k}{2}$

$b= \frac{k}{5}$

$c= \frac{k}{3}$

$\frac{k}{2}+\frac{k}{5}+ \frac{k}{3}=930 || \hbox{ Aducem la acelasi numitor : 30}$

$\frac{15k}{30}+ \frac{10k}{30}+ \frac{6k}{30}= \frac{27.900}{30} || \hbox{ Inmultim relatia cu 30 }$

$15k+10k+6k=27.900$
$31k=27.900$ ⇒ $\boxed {k=900}$

$a= \frac{900}{2}$ ⇒ $\boxed {\boxed {a=450}}$

$b= \frac{900}{5}$ ⇒ $\boxed{\boxed{b=180}}$

$c= \frac{900}{3}$ ⇒ $\boxed{\boxed{c=300}}$

Answer 2

a/5/10=b/2/10=c/3/9
⇒a/5/10+b/2/10+c/3/9=930/7/10+3/9⇒930/63/90+30/90⇒930/93/90⇒930/31/30⇒
930·30/31⇒30·30=900k
⇒a=900·0,5⇒a=900·5/10⇒a=90·5⇒a=450;
⇒b=900·0,2⇒b=900·2/10⇒b=90·2⇒180;
⇒c=900·3/9⇒c=100·3⇒c=300;
Verificare 450+180+300=630+300=930;