Question

[Trương Ngọc Linh]

\(4x=3y=2z\) \(và\) \(x+y+z=65\)

Answer 1

[Nguyễn Thị Thương Hoài]

4\(x\) = 3y = 2z 

\(x=\dfrac{3y}{4}\); z = \(\dfrac{3y}{2}\)

Thay \(x=\dfrac{3y}{4};z=\dfrac{3y}{2}\) vào biểu thức \(x+y+z\) = 65

Ta có: \(\dfrac{3y}{4}+y+\dfrac{3y}{2}=65\)

          y.(\(\dfrac{3}{4}+1+\dfrac{3}{2}\)) = 65

        y.\(\dfrac{13}{4}\) = 65

       y = 65 : \(\dfrac{13}{4}\)

       y = 20 

\(x\) = 20 x \(\dfrac{3}{4}\) = 15

z = 20 x \(\dfrac{3}{2}\) = 30

Vậy (\(x;y;z\)) = (15; 20; 30)

Answer 2

[Akai Haruma]

Lời giải:

Áp dụng TCDTSBN:

$4x=3y=2z=\frac{x}{\frac{1}{4}}=\frac{y}{\frac{1}{3}}=\frac{z}{\frac{1}{2}}=\frac{x+y+z}{\frac{1}{4}+\frac{1}{3}+\frac{1}{2}}=\frac{65}{\frac{13}{12}}=60$

$\Rightarrow x=60:4=15; y=60:3=20; z=60:2=30$