$\text{Có $\dfrac{x}{2}$ = $\dfrac{2y}{5}$ = $\dfrac{4z}{7}$}$
$\text{⇒ $\dfrac{x}{2}$ × $\dfrac{1}{4}$ = $\dfrac{2y}{5}$ × $\dfrac{1}{4}$}$
$\text{= $\dfrac{4z}{7}$ ×$\dfrac{1}{4}$}$
$\text{⇒$\dfrac{x}{8}$ = $\dfrac{y}{10}$ = $\dfrac{z}{7}$}$
$\text{⇔$\dfrac{3x}{24}$ = $\dfrac{5y}{50}$ = $\dfrac{7z}{49}$}$
$\text{Áp dụng tính chất dãy tỉ số bằng nhau ta có:}$
$\text{$\dfrac{3x}{24}$ = $\dfrac{5y}{50}$ = $\dfrac{7z}{49}$}$
$\text{= $\dfrac{3x + 5y + 7z}{24 + 50 + 49}$=$\dfrac{123}{123}$=1}$
$\text{Do đó:}$
$\dfrac{3x}{24}$ = 1⇔ $\dfrac{x}{8}$ = 1 ⇒ x = 8
$\dfrac{5y}{50}$ = 1⇔ $\dfrac{y}{10}$ = 1 ⇒ y = 10
$\dfrac{7z}{49}$ = 1⇔ $\dfrac{z}{7}$ = 1 ⇒ z = 7
$\text{Vậy x = 8; y = 10; z = 7}$
