Question

[Nguyễn Lương Phương Vy]

Mọi người giúp mik giải với😢

Answer 1

[VuongTung10x]

\(\frac{x}{5}=\frac{y}{4}=\frac{z}{7},x+2y+z=10\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có 

\(\frac{x}{5}=\frac{y}{4}=\frac{z}{7}=\frac{x+2y+z}{5+4\cdot2+7}=\frac{10}{20}=\frac{1}{2}\)

\(\frac{x}{5}=\frac{1}{2}\Rightarrow x=5\cdot\frac{1}{2}=2.5\)

\(\frac{x}{4}=\frac{1}{2}\Rightarrow x=4\cdot\frac{1}{2}=2\)

\(\frac{z}{7}=\frac{1}{2}\Rightarrow z=7\cdot\frac{1}{2}=3.5\)

b \(\frac{x}{4}=\frac{y}{5}=\frac{z}{2},x+y=18\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có : 

\(\frac{x}{4}=\frac{y}{5}=\frac{z}{2}=\frac{x+y}{4+5}=\frac{18}{9}=2\)

\(\frac{x}{4}=2\Rightarrow x=8\)

\(\frac{y}{5}=2\Rightarrow y=10\)

\(\frac{z}{2}=2\Rightarrow z=4\)

c,\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5},,5x-z=20\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=\frac{5x-z}{2\cdot5-5}=\frac{20}{5}=4\)

\(\frac{x}{2}=4\Rightarrow x=8\)

\(\frac{y}{3}=4\Rightarrow y=12\)

\(\frac{z}{5}=4\Rightarrow z=20\)

d,\(\frac{x}{2}=\frac{y}{3}=\frac{z}{4},2x+y-z=9\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có :

\(\frac{x}{2}=\frac{y}{3}=\frac{z}{4}=\frac{2x+y-z}{2\cdot2+3-4}=\frac{9}{3}=3\)

\(\frac{x}{2}=3\Rightarrow x=6\)

\(\frac{y}{3}=3\Rightarrow y=9\)

\(\frac{z}{4}=3\Rightarrow z=12\)

Answer 2

[VuongTung10x]

\(2x=3y=5z,x-2y+3x=65\)

Ta có :

\(\frac{2x}{30}=\frac{3y}{30}=\frac{5z}{30}\)\(=\frac{x}{15}=\frac{y}{10}=\frac{z}{6}\)

Áp dụng tc dtsbn ta có :

\(\frac{x}{15}=\frac{y}{10}=\frac{z}{6}=\frac{x-2y+3z}{15-2\cdot10+3\cdot6}=\frac{65}{13}=5\)

\(\frac{x}{15}=5\Rightarrow x=75\)

\(\frac{y}{10}=5\Rightarrow y=50\)

\(\frac{z}{6}=5\Rightarrow z=30\)

v,

\(1x=3y\Rightarrow\frac{x}{3}=\frac{y}{1}\)

\(3y=4z\Rightarrow\frac{y}{4}=\frac{z}{3}\)

\(\frac{\Rightarrow x}{12}=\frac{y}{4}=\frac{z}{3}\)

ADTCDTSBNTC :

\(\frac{x}{12}=\frac{y}{4}=\frac{z}{3}=\frac{2x-y-z}{2\cdot12-4-3}=\frac{170}{17}=10\)

\(\frac{x}{12}=10\Rightarrow x=120\)

\(\frac{y}{4}=10\Rightarrow y=40\)

\(\frac{z}{3}=10\Rightarrow z=30\)

w, \(\frac{3x}{60}=\frac{4y}{60}=\frac{5z}{60}\)

\(=\frac{x}{20}=\frac{y}{15}=\frac{z}{12}\)

ADTCDTSBNTC :

\(\frac{x}{20}=\frac{y}{15}=\frac{z}{12}=\frac{x-y+z}{20-15+12}=\frac{85}{17}=5\)

\(\frac{x}{20}=5\Rightarrow x=100\)

\(\frac{y}{15}=5\Rightarrow y=75\)

\(\frac{z}{12}=5\Rightarrow z=60\)

x, \(\frac{x}{5}=\frac{y}{3};\frac{y}{7}=\frac{z}{4}\)và x+y-z=132 

Ta có : \(\frac{x}{35}=\frac{y}{21}=\frac{z}{12}\)

ADTCDTSBNTC :

\(\frac{x}{35}=\frac{y}{21}=\frac{z}{12}=\frac{x+y-z}{35+21-12}=\frac{132}{44}=3\)

\(\frac{x}{35}=3\Rightarrow x=105\)

\(\frac{y}{21}=3\Rightarrow y=63\)

\(\frac{z}{12}=3\Rightarrow z=36\)