Question

Dividir 1.090 em partes inversamente proporcionais a 2/3, 4/5 e 7/8.

Answer 1

Partes --> A   B   C
Inversas--> 3/2   5/4    8/7
A+B+C = 1090
3/2 + 5/4 + 8/7 = ---mmc(2,4,7) = 28
42/28 + 35/28 + 32/28 = 109/28 . Então:

$\frac{A}{ \frac{3}{2} }= \frac{B}{ \frac{5}{4} }= \frac{C}{ \frac{8}{7} }= \frac{1090}{ \frac{109}{28} }=1090. \frac{28}{109} =280$

$\frac{A}{ \frac{3}{2} }=280<==>A=280. \frac{3}{2}=420$

$\frac{B}{ \frac{5}{4} } =280<==>B= \frac{5}{4}.280=350$

$\frac{C}{ \frac{8}{7} }=280<==>C= \frac{8}{7}.280=320$

As partes são : 420 + 350 + 320 = 1090