Question

Tìm các số x, y, z biết:

\(\frac{x}{10}=\frac{y}{5};\frac{y}{2}=\frac{z}{3}\) và \(2x-3y+4z=330\)

Answer 1

\(\frac{x}{10}=\frac{y}{5}\Rightarrow\frac{x}{20}=\frac{y}{10}\)

\(\frac{y}{2}=\frac{z}{3}\Rightarrow\frac{y}{10}=\frac{z}{15}\)

\(\Rightarrow\frac{x}{20}=\frac{y}{10}=\frac{z}{15}=\frac{2x}{40}=\frac{3y}{30}=\frac{4z}{60}=\frac{2x-3y+4z}{40-30+60}=\frac{330}{70}=\frac{33}{7}\)

(tính chất dãy tỉ số bằng nhau)

\(\Rightarrow x=\frac{33}{7}.20;\text{ }y=\frac{33}{7}.10;\text{ }z=\frac{33}{7}.15\)

Answer 2

Ta có: \(\frac{x}{10}=\frac{y}{5}\Rightarrow\frac{x}{20}=\frac{y}{10};\frac{y}{2}=\frac{z}{3}\Rightarrow\frac{y}{10}=\frac{z}{15}\)

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

\(\frac{x}{20}=\frac{y}{10}=\frac{z}{15}=\frac{2x}{40}=\frac{3y}{30}=\frac{4z}{60}=\frac{2x-3y+4z}{40-30+60}=\frac{330}{70}=\frac{33}{7}\)

\(\frac{x}{20}=\frac{33}{7}\Rightarrow x=\frac{33\times20}{7}=\frac{660}{7}\)

\(\frac{y}{10}=\frac{33}{7}\Rightarrow y=\frac{33\times10}{7}=\frac{330}{7}\)

\(\frac{z}{15}=\frac{33}{7}\Rightarrow z=\frac{33\times15}{7}=\frac{495}{7}\)

Answer 3

\(\frac{x}{10}=\frac{y}{5}\Rightarrow\frac{1}{2}.\frac{x}{10}=\frac{1}{2}.\frac{y}{5}=\frac{x}{20}=\frac{y}{10}\)

\(\frac{y}{2}=\frac{z}{3}=\frac{1}{5}.\frac{y}{2}=\frac{1}{5}.\frac{z}{3}=\frac{y}{10}=\frac{z}{15}\)

\(\Rightarrow\frac{x}{20}=\frac{y}{10}=\frac{z}{15}\)

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

\(\frac{x}{20}=\frac{y}{10}=\frac{z}{15}=\frac{2x}{40}=\frac{3y}{30}=\frac{4z}{60}\Rightarrow\frac{2x-3y+4z}{40-30+60}\)\(=\frac{330}{70}=\frac{33}{7}\)

\(\frac{x}{20}=\frac{33}{7}\Rightarrow x=\frac{33.20}{7}=\frac{660}{7}\)

\(\frac{y}{10}=\frac{33}{7}\Rightarrow y=\frac{33.10}{7}=\frac{330}{7}\)

\(\frac{z}{15}=\frac{33}{7}\Rightarrow z=\frac{33.15}{7}=\frac{495}{7}\)

Vậy....