Question

Fie proportiile x/y = 1,(3) si 4a-b/4a+b=2/5 A) aratati ca 3x-2y /x = 3/2. b) aflati raportul a si b

Answer 1

$\displaystyle{ \frac{x}{y} = 1,(3) = \frac{13-1}{9} = \frac{12}{9} = \frac{4}{3} }$

$\displaystyle{ \rightarrow 3x = 4y \rightarrow x = \frac{4y}{3} }$

$\displaystyle{ \frac{3x-2y}{x} = \frac{4y-2y}{\frac{4y}{3} } = 2y \cdot \frac{3}{4y} }$

$\displaystyle{ = \frac{6y}{4y} = \frac{6}{4}^{(2} = \frac{3}{2} }$

$\displaystyle{ \frac{4a-b}{4a + b} = \frac{2}{5} }$

$\displaystyle{ 2 \cdot (4a + b) = 5 \cdot (4a - b) }$

$\displaystyle{ 8a + 2b = 20a - 5b }$

$\displaystyle{ 2b = 12a - 5b }$

$\displaystyle{ 12a - 7b = 0}$

$\displaystyle{ 12a = 7b }$

$\displaystyle{ \frac{a}{b} = \frac{7}{12} }$