Question

divida 84 em partes inversamente proporcionais a 3 e 4​

Answer 1

$\frac{a}{ \frac{1}{3} } = \frac{b}{ \frac{1}{4} } = k \\ a = \frac{k}{3} \\ b = \frac{k}{4}$

$a + b = 84 \\ \frac{k}{3} + \frac{k}{4} = 84 \\ \frac{4k + 3k = 1008}{12} \\ 7k = 1008$

$k = \frac{1008}{7} \\ k = 144$

$a = \frac{144}{3} = 48 \\ b = \frac{144}{4} = 36$