Question

divida 102 em partes inversamente proporcionais a 6,8 e 20

Answer 1

$\frac{x}{ \frac{1}{6} } = \frac{y}{ \frac{1}{8} } = \frac{z}{ \frac{1}{20} } = \frac{x+y+z}{ \frac{1}{6}+\frac{1}{8}+\frac{1}{20} } = \frac{102}{\frac{41}{120}} = \frac{12240}{41}$

$\frac{x}{ \frac{1}{6} } = \frac{12240}{41} \\ 41x = 2040 \Rightarrow x = \frac{2040}{41}$

$\frac{y}{ \frac{1}{8} } = \frac{12240}{41} \\ 41y = 1530 \Rightarrow y = \frac{1530}{41}$

$\frac{z}{ \frac{1}{20} } = \frac{12240}{41} \\ 41z = 612 \Rightarrow z = \frac{612}{41}$

R: $\frac{2040}{41} , \frac{1530}{41}, \frac{612}{41}$