Question

divida o numero 180 em partes inversamente proporcionais 4 e 6

Answer 1

$a+b=180$

$\dfrac{a}{\frac{1}{4}}=\dfrac{b}{\frac{1}{6}} \iff 4a=6b \iff 2a=3b \iff a=\dfrac{3b}{2}$

Substituindo na primeira equação:

$a+b=180 \iff \dfrac{3b}{2}+b=180 \iff 3b+2b=360 \iff 5b=360$

$b=\dfrac{360}{5} \iff \boxed{b=72}$

$a=\dfrac{3b}{2} \iff a=\dfrac{3\cdot72}{2} \iff a=\dfrac{216}{2} \iff \boxed{a=108}$

108 e 72