Question

Raportul numerelor x si y este 0,(8).
Sa se afle2x+5y supra 3x-2y .

Answer 1

$\dfrac{x}{y} = 0,(8) \Rightarrow \dfrac{x}{y} = \dfrac{8}{9} \\ \\ \Rightarrow x = \dfrac{8}{9}\cdot y \\ \\ \\ \dfrac{2x+5y}{3x-2y}= \dfrac{2\cdot \dfrac{8}{9}\cdot y +5y}{3\cdot \dfrac{8}{9}\cdot y - 2y } = \dfrac{ \dfrac{16y+5\cdot 9y}{9} }{\dfrac{8y-2\cdot 3y}{3} } =\dfrac{16y+45y}{9} \cdot \dfrac{3}{8y-6y}= \\ \\ \\ = \dfrac{61y}{3}\cdot \dfrac{1}{2y} = \dfrac{61}{6} \\ \\ \Rightarrow \boxed{ \dfrac{2x+5y}{3x-2y}= \dfrac{61}{6} }$