Question

Fie a , b ∈ Q* , astfel incat $\frac{3a + 2b}{a + 7b}$ = $\frac{12}{23}$ . Determinati valoarea raportului $\frac{a}{b}$.
Multumesc.

Answer 1

$\it Not\breve{a}m\ \dfrac{a}{b} =k \Rightarrow a= bk$

Raportul din enunț devine:

[tex]\it \dfrac{3\cdotbk+2b}{bk+7b} = \dfrac{12}{23} \Rightarrow \dfrac{b(3k+2)}{b(k+7)} = \dfrac{12}{23} \Rightarrow \dfrac{3k+2}{k+7} = \dfrac{12}{23} \Rightarrow \\\;\\ \\\;\\ \Rightarrow 23(3k+2)=12(k+7) \Rightarrow 69k+46 = 12k+84 \Rightarrow \\\;\\ \\\;\\ \Rightarrow 69k-12k=84-46 \Rightarrow 57k=38\Rightarrow k = \dfrac{38}{57}[/tex]