Question

Dacă:
$\frac{2a + 3b}{3a + 2b} = \frac{5}{11}$
, atunci
$\frac{a}{b} =$
este: A-
$\frac{11}{17}$
; B-
$\frac{1}{2}$
; C-
$\frac{5}{12}$
sau D-
$\frac{24}{7}$
?????​

Answer 1

$\dfrac{2a+3b}{3a+2b} = \dfrac{5}{11} \Rightarrow \dfrac{\dfrac{1}{b}\Big(2a+3b\Big)}{\dfrac{1}{b}\Big(3a+2b\Big)} =\dfrac{5}{11} \Rightarrow\dfrac{2\cdot \dfrac{a}{b}+3}{3\cdot \dfrac{a}{b}+2} = \dfrac{5}{11} \\ \\ \dfrac{a}{b} = x \Rightarrow \dfrac{2x+3}{3x+2} = \dfrac{5}{11} \Rightarrow 11(2x+3) = 5(3x+2) \Rightarrow \\ \\ \Rightarrow 22x+33 = 15x+10\Rightarrow 7x = -23 \Rightarrow x = -\dfrac{23}{7} \Rightarrow \boxed{\dfrac{a}{b} = - \dfrac{23}{7}}$