Question

Ex 4. Va rog sa mi explicati si mie cum se face

Answer 1

$\frac{6x}{5y} = \frac{4}{5}$

$6 \times 5x = 4 \times 5y$

$6x = 4y$

$3x = 2y = k$

$x = \frac{k}{3}$

$y = \frac{k}{2}$

$\frac{7x + 2y}{5x - 2y} = \frac{7 \times \frac{k}{3} + 2 \times \frac{k}{2} }{5\times \frac{k}{3} - 2 \times \frac{k}{2} } = \frac{ \frac{7k}{3} + k}{ \frac{5k}{3} - k } = \frac{ \frac{7k}{3} + \frac{3k}{3} }{ \frac{5k}{3} - \frac{3k}{3} } = \frac{ \frac{10k}{3} }{ \frac{2k}{3} } = \frac{10k}{3} \div \frac{2k}{3} = \frac{10k}{3} \times \frac{3}{2k} = 5$