Question

Divida 220 em partes inversamente proporcionais a 2, 3 e 1/3

Answer 1

Seja "x" o coeficiente de proporcionalidade, temos:

--> Parte inversamente proporcional a 2:    $\frac{x}{2}$

--> Parte inversamente proporcional a 3:    $\frac{x}{3}$

--> Parte inversamente proporcional a 2:    $\frac{x}{\frac{1}{3}}=3x$

A soma das tres partes deve valer 220, logo:

    $\frac{x}{2}+\frac{x}{3}+3x=220\\\\\\MMC=2~.~3=6\\\\\frac{3~.~x~+~2~.~x~+~3x~.~6}{6}=220\\\\\\3x+2x+18x=6~.~220\\\\\\23x=1320\\\\\\x=\frac{1320}{23}$

Assim, as partes valem:

  $\rightarrow \frac{x}{2}=\frac{1320}{23~.~2}=\boxed{\frac{660}{23}}\\\\\rightarrow \frac{x}{3}=\frac{1320}{23~.~3}=\boxed{\frac{440}{23}}\\\\\rightarrow 3x=3~.~\frac{1320}{23}=\boxed{\frac{3960}{23}}$