Question

X a) Ştiind că x supra y = 0,(4), calculați raportul 3x+2y supra 5x-2y​

Answer 1

$\tfrac{x}{y} = \frac{4}{9} \\ x = \tfrac{4y}{9} \\ \\ \underline{Rezolvare}:\\ \tfrac{3x + 2y}{5x - 2y} = \tfrac{3 \times \frac{4y}{9} + 2y }{5 \times \frac{4y}{9} - 2y } = \tfrac{ \frac{4y}{3} + 2y}{ \frac{20y}{9} - 2y } = \frac{ \frac{4y + 6y}{3} }{ \frac{20y - 18y}{9} } \\ = \tfrac{10y}{3} \times \tfrac{9}{2y} = 5 \times 3 = \boxed{15}$

Answer 2

Explicație pas cu pas:

$0.(4) = \dfrac{4}{9} \implies \dfrac{x}{y} = \dfrac{4}{9} \\ \dfrac{x}{4} = \dfrac{y}{9} = k \\ x = 4k \ \ si \ \ y = 9k$

$\dfrac{3x + 2y}{5x - 2y} = \dfrac{3 \cdot 4k + 2 \cdot 9k}{5 \cdot 4k - 2 \cdot 9k} =$

$= \dfrac{12k + 18k}{20k - 18k} = \dfrac{30k}{2k} = 15$