Bổ xung cách 2:
Xét $\dfrac{2x}{3}=\dfrac{3y}{4} $
$⇒\dfrac{x}{1,5}=\dfrac{y}{\dfrac{4}{3}}(1)$
Xét $\dfrac{3y}{4}=\dfrac{4z}{5}$
$⇒\dfrac{y}{\dfrac{4}{3}}=\dfrac{z}{\dfrac{5}{4}} (2)$
Từ $(1)(2)⇒\dfrac{x}{1,5}=\dfrac{y}{\dfrac{4}{3}}=\dfrac{z}{\dfrac{5}{4}} $
Áp dụng T/C dãy tỉ số = nhau :
$⇒\dfrac{x}{1,5}=\dfrac{y}{\dfrac{4}{3}}=\dfrac{z}{\dfrac{5}{4}} =\dfrac{x+y+z}{1,5+\dfrac{4}{3}+\dfrac{5}{4}}=\dfrac{49}{\dfrac{49}{12}}=12$
Do đó:
$\dfrac{2x}{3}=12⇒x=18$
$\dfrac{3y}{4}=12⇒y=16$
$\dfrac{4z}{5}=12⇒z=15$
Vậy $(x,y,z)=(18,16,15)$
