Question

\(\dfrac{x}{5}\)=\(\dfrac{y}{6}\)=\(\dfrac{z}{7}\) và x + y + z=36

\(\dfrac{x}{2}\)=\(\dfrac{y}{3}\)=\(\dfrac{z}{6}\)và 3x - 2y +2z =24

Answer 1

ta có

\(\dfrac{x}{5}=\dfrac{y}{6}=\dfrac{z}{7}\) và x+y+z=36

áp dụng tính chất của dãy tỉ số bằng nhau 

\(\dfrac{x}{5}=\dfrac{y}{6}=\dfrac{z}{7}=\dfrac{x+y+z}{5+6+7}=\dfrac{36}{18}=2\)

mà

\(\dfrac{x}{5}=2\rightarrow x=2.5=10\\ \dfrac{y}{6}=2\rightarrow y=2.6=12\\ \dfrac{z}{7}=2\rightarrow z=2.7=14\)

vậy ......

-------------------------------

ta có

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{6}\) và 3x-2y+2z=24

áp dụng tính chất của dãy tỉ số bằng nhau, có

\(\dfrac{x}{2}=\dfrac{y}{2}=\dfrac{z}{6}=\dfrac{3x-2y+2z}{3.2-2.3+2.6}=\dfrac{24}{12}=2\)

mà

\(\dfrac{x}{2}=2\rightarrow x=2.2=4\\ \dfrac{y}{3}=2\rightarrow y=2.3=6\\ \dfrac{z}{6}=2\rightarrow z=2.6=12\)

vậy ......

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

1) \(\dfrac{x}{5}=\dfrac{y}{6}\Rightarrow y=\dfrac{6x}{5}\)

\(\dfrac{x}{5}=\dfrac{z}{7}\Rightarrow z=\dfrac{7x}{5}\)

\(x+y+z=36\Leftrightarrow x+\dfrac{6x}{5}+\dfrac{7x}{5}=36\Leftrightarrow x\left(1+\dfrac{6}{5}+\dfrac{7}{5}\right)=36\Leftrightarrow\dfrac{18}{5}x=36\Leftrightarrow x=10\)

Vậy x = 10 , y = 12 , z = 14

2) \(\dfrac{x}{2}=\dfrac{y}{3}\Rightarrow y=\dfrac{3x}{2}\)

\(\dfrac{x}{2}=\dfrac{z}{6}\Rightarrow z=\dfrac{6x}{2}\)

\(3x-2y+2z=24\Leftrightarrow3x-\dfrac{2.3x}{2}+\dfrac{2.6x}{2}=24\Leftrightarrow3x-3x+6x=24\Leftrightarrow x=4\)

Vậy x = 4 , y = 6 , z = 12