Question

Buna ! Afla valoarea raportului 2a+5b/3b+10c daca numerele a,b,c sunt direct proportioanle cu 0,(3) ; 0,0(3) ; 0,00(3).

Mersi !!

Answer 1

{a,b,c}~d.{0,(3);0,0(3);0,00(3)} putem sa scriem in felul urmator: 
$\frac{a}{0,(3)}= \frac{b}{0,0(3)}= \frac{c}{0,00(3)}=t$ am egalat tot sirul cu un numar natural t.Iar acum facem in felul urmator:
$\frac{a}{0,(3)}=t=\ \textgreater \ a=0,(3)\cdot t~sau~a= \frac{3}{9}t \\ \frac{b}{0,0(3)}=t=\ \textgreater \ b=0,0(3)\cdot t~sau~b= \frac{3}{90}t \\ \frac{c}{0,00(3)}=t=\ \textgreater \ c=0,00(3)\cdot t~sau~c= \frac{3}{900}t$ iar acum inlocuim in relatia $\frac{2a+5b}{3b+10c}$ si obtinem:$\frac{2\cdot \frac{3}{9}t+10\cdot \frac{3}{900}t }{3\cdot \frac{3}{90}t+10\cdot \frac{3}{900}t }= \frac{ \frac{6}{9}t+ \frac{30}{900}t }{ \frac{9}{90}t+ \frac{30}{900}t }= \frac{ \frac{630}{900}t }{ \frac{120}{900}t }= \frac{630}{120}= \frac{21}{4}$