Question

divida o número 600 em partes inversamente proporcional a 6,2,3 e 18

Answer 1

$\frac{w}{ \frac{1}{2}} = \frac{x}{ \frac{1}{3}} = \frac{y}{ \frac{1}{6}} = \frac{z}{ \frac{1}{18}} = k \\ \\ \frac{w+x+y+z}{ \frac{1}{2} + \frac{1}{3}+\frac{1}{6} + \frac{1}{18} } = k \\ \\ \frac{600}{ \frac{9 + 6 +3+1}{18} } = k \\ \\ k = \frac{600}{\frac{19}{18}} \\ \\ \boxed{k = \frac{300}{19}}$


$2w = k \\ \\ \boxed{\boxed{w = \frac{150}{19}}} \\ \\ \\ 3x = k \\ \\ \boxed{\boxed{x = \frac{100}{19}}} \\ \\ \\ 6y = k \\ \\ \boxed{\boxed{y= \frac{50}{19}}} \\ \\ \\ 18z = k \\ \\ \boxed{\boxed{z = \frac{50}{114}}}$