Question

Divida 2870 em três parcelas inversamente proporcionais a 2,3 e 7.

Answer 1

$\frac{x}{2} + \frac{x}{3} + \frac{x}{7} =2870 \\ \\ 42 \frac{x}{2} +42. \frac{x}{3} +42. \frac{x}{7} =42.2870 \\ \\ 21x+14x+6x=120540 \\ \\ 41x=120540 \\ \\ x=2940 \\ \\ \\ \frac{x}{2} = \frac{2940}{2} =1470 \\ \\ \frac{x}{3} = \frac{2940}{3} =980 \\ \\ \frac{x}{7} = \frac{2940}{7} =420$

Resposta 1470; 980; 420

Answer 2

$x = \dfrac{2870}{ \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{7}} \\ \\ \\ x = \dfrac{2870}{ \dfrac{41}{42}} \\ \\ \\ x = \dfrac{2870 . 42}{41} \\ \\ \\ x = \dfrac{120540}{41} \\ \\ \\ x = 2940$

x =  coeficiente de proporcionalidade, multiplicar pelas frações correspondentes dadas no problema (inversamente)

$2940 * \dfrac{1}{2} =\ \textgreater \ \dfrac{2940}{2} = 1470 \\ \\ \\ 2940 * \dfrac{1}{3} =\ \textgreater \ \dfrac{2940}{3} = 980 \\ \\ \\ 2940 * \dfrac{1}{7} =\ \textgreater \ \dfrac{2940}{7} = 420$