Question

[Võ Ngọc Vân Anh]

Tìm x,y,z, biết : 

a) \(\frac{x}{y}=\frac{6}{9}\) và x - y = 30  

b)\(\frac{x}{5}=\frac{y}{4}=\frac{z}{7}\) và x + 2y + z =40  

c)\(\frac{x}{3}=\frac{y}{4}\); \(\frac{z}{5}=\frac{y}{7}\) và 2x + 3y - z = 106

Answer 1

[Phạm Duy Quý]

ta có : \(\frac{x}{y}=\frac{6}{9}\)

\(\Rightarrow\frac{x}{6}=\frac{y}{9}\)\(=\frac{x-y}{6-9}\)\(=\frac{30}{-3}\)= \(-10\)

\(\frac{x}{6}=-10\Rightarrow x=-60\)

\(\frac{y}{9}=-10\Rightarrow y=-90\)

b) \(\frac{x}{5}=\frac{y}{4}=\frac{z}{7}=\frac{x}{5}=\frac{2y}{8}=\frac{z}{7}=\frac{x+2y+z}{5+8+7}=\frac{40}{20}=2\)

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

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

\(\frac{z}{7}=2\Rightarrow z=14\)

C) ta có \(\frac{x}{3}=\frac{y}{4}\)

\(\Rightarrow\frac{x}{3}.\frac{1}{7}=\frac{y}{4}.\frac{1}{7}\)

\(\frac{x}{21}=\frac{y}{28}\)

ta lại có \(\frac{z}{5}=\frac{y}{7}\)

\(\Rightarrow\frac{z}{5}.\frac{1}{4}=\frac{y}{7}.\frac{1}{4}\)

\(\frac{z}{20}=\frac{y}{28}\)

\(\Rightarrow\frac{z}{20}=\frac{y}{28}=\frac{x}{21}\)\(=\frac{2x}{42}=\frac{3y}{84}=\frac{z}{20}=\frac{2x+3y-z}{42+84-20}=\frac{106}{106}=1\)

\(\frac{x}{21}=1\Rightarrow x=21\)

\(\frac{y}{28}=1\Rightarrow y=28\)

\(\frac{z}{20}=1\Rightarrow z=20\)

chúc bn hc tốt ^-^