Question

stiind că x supra y =3 supra 2 , determină valoarea rapoartelor

Answer 1

$\frac{x}{y} = \frac{3}{2}$

$2x = 3y = > x = \frac{3y}{2}$

$a) \frac{2x + 3y}{7x - 4y} = \frac{2 \times \frac{3y}{2} + 3y}{7 \times \frac{3y}{2} - 4y} = \frac{3y + 3y}{ \frac{21y}{2} - 4y }$

$= \frac{6y}{ \frac{21y}{2} - \frac{8y}{2} } = \frac{6y}{ \frac{21y - 8y}{2} } = \frac{6y}{ \frac{13y}{2} }$

$= 6y \times \frac{2}{13y} = \frac{12y}{13y} = \frac{12}{13}$

$b) \frac{7x - 4y}{x + 2y} = \frac{7 \times \frac{3y}{2} - 4y }{ \frac{3y}{2} + 2y} = \frac{ \frac{21y}{2} - 4y}{ \frac{3y}{2} + \frac{4y}{2} }$

$= \frac{ \frac{21y}{2} - \frac{8y}{2} }{ \frac{3y + 4y}{2} } = \frac{ \frac{21y - 8y}{2} }{ \frac{7y}{2} } = \frac{ \frac{13y}{2} }{ \frac{7y}{2} } = \frac{13y}{2} \times \frac{2}{7y} = \frac{13y}{7y} = \frac{13}{7}$

$c) \frac{3x + 5y}{2x + 7y} = \frac{3 \times \frac{3y}{2} + 5y}{2 \times \frac{3y}{2} + 7y } = \frac{ \frac{9y}{2} + 5y }{3y + 7y}$

$= \frac{ \frac{9y}{2} + \frac{10y}{2} }{10y} = \frac{ \frac{9y + 10y}{2} }{10y} = \frac{ \frac{19y}{2} }{10y}$

$= \frac{19y}{2} \times \frac{1}{10y} = \frac{19y}{20y} = \frac{19}{20}$