Question

va rog ajutați mă 1,2,3.mersi

Answer 1

$1) \frac{x}{y} = \frac{2}{3}$

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

$\frac{6x + y}{9x + 3y} = \frac{6 \times \frac{2y}{3} +y }{9 \times \frac{2y}{3} + 3y } = \frac{4y + y}{6y + 3y} = \frac{5y}{9y} = \frac{5}{9}$

$= > a) \frac{5}{9}$

$2) \frac{a}{b} = \frac{c}{d} = \frac{e}{f} = \frac{7}{5}$

$\frac{e}{f} = \frac{7}{5}$

$5e = 7f = > e = \frac{7f}{5}$

$\frac{c}{d} = \frac{e}{f}$

$cf = de$

$cf = \frac{7df}{5}$

$5cf = 7df \: | \div f$

$5c = 7d = > c = \frac{7d}{5}$

$\frac{a}{b} = \frac{c}{d}$

$\frac{a}{b} = \frac{ \frac{7d}{5} }{d}$

$ad = \frac{7db}{5}$

$5ad = 7db \: | \div d$

$5a = 7b = > a = \frac{7b}{5}$

$\frac{a + c + e}{b + d + f} = \frac{ \frac{7b}{5} + \frac{7d}{5} + \frac{7f}{5} }{b + d + f} = \frac{ \frac{7b + 7d + 7f}{5} }{b + d + f}$

$= \frac{ \frac{7(b + d + f)}{5} }{b + d + f} = \frac{7(b + d + f)}{5} \times \frac{1}{b + d + f}$

$= \frac{7(b + d + f)}{5(b + d + f)} = \frac{7}{5}$

$= > c) \frac{7}{5}$

$3) \frac{1 + 2 + 3 + ... + 100}{25} = \frac{x}{3}$

$\frac{ \frac{100(100 + 1)}{2} }{25} = \frac{x}{3}$

$\frac{ \frac{100 \times 101}{2} }{25} = \frac{x}{3}$

$\frac{50 \times 101}{25} = \frac{x}{3}$

$2 \times 101 = \frac{x}{3}$

$202 = \frac{x}{3}$

$x = 202 \times 3$

$x = 606$

$= > c)606$