Question

Divida o número 301 em partes inversamente proporcionais a 5, 7 e 15.

Answer 1

Explicação passo-a-passo:

Sejam x, y e z essas partes

=> $\sf x+y+z=301$

=> $\sf 5x=7y=15z$

• $\sf 5x=7y~\Rightarrow~y=\dfrac{5x}{7}$

• $\sf 5x=15z~\Rightarrow~z=\dfrac{5x}{15}~\Rightarrow~z=\dfrac{x}{3}$

Substituindo $\sf y~por~\dfrac{5x}{7}~e~z~por~\dfrac{x}{3}$ em $\sf x+y+z=301$:

$\sf x+\dfrac{5x}{7}+\dfrac{x}{3}=301$

$\sf 21\cdot x+3\cdot5x+7\cdot x=21\cdot301$

$\sf 21x+15x+7x=6321$

$\sf 43x=6321$

$\sf x=\dfrac{6321}{43}$

$\sf \red{x=147}$

Logo:

=> $\sf y=\dfrac{5x}{7}$

$\sf y=\dfrac{5\cdot147}{7}$

$\sf y=\dfrac{735}{7}$

$\sf \red{y=105}$

=> $\sf z=\dfrac{x}{3}$

$\sf z=\dfrac{147}{7}$

$\sf \red{z=49}$