Question

Três naturais x, y e z são tais que 3x-y+2z=156 e $\frac{x}{2} = \frac{y}{3}=\frac{z}{5}$

Logo x+y+z
igual a

a) 100.

b) 110.

c) 116.

d) 120.

e) 144.

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\sf{3x - y + 2z = 156}$

$\sf{\dfrac{x}{2} = \dfrac{y}{3} = \dfrac{z}{5}}$

$\sf{y = \dfrac{3x}{2}}$

$\sf{z = \dfrac{5x}{2}}$

$\sf{3x - \dfrac{3x}{2} + 2\:.\:\dfrac{5x}{2} = 156}$

$\sf{6x - 3x + 10x = 312}$

$\sf{13x = 312}$

$\sf{x = 24}$

$\sf{y = 36}$

$\sf{z = 60}$

$\sf{x + y + z = 24 + 36 + 60}$

$\boxed{\boxed{\sf{x + y + z = 120}}}\leftarrow\textsf{letra D}$