Question

tim x , y, z        biet,\(\frac{z}{4}=\frac{y}{3};\frac{x}{2}=\frac{z}{5}\)                   va x+y+z=51

Answer 1

\(\frac{z}{4}=\frac{y}{3}\Rightarrow\frac{z}{20}=\frac{y}{15}^{\left(1\right)}\)

\(\frac{x}{2}=\frac{z}{5}\Rightarrow\frac{x}{8}=\frac{z}{20}^{\left(2\right)}\)

\(\left(1\right),\left(2\right)\Rightarrow\frac{x}{8}=\frac{z}{20}=\frac{y}{15}\)

Áp dụng tính chất dãy tỉ số bằng nhau:

\(\frac{x}{8}=\frac{z}{20}=\frac{y}{15}=\frac{x+y+z}{8+20+15}=\frac{51}{43}\)

..... ( tới bước này bạn tự làm tiếp nhá )

Answer 2

\(\frac{z}{4}=\frac{y}{3}\Rightarrow\frac{z}{20}=\frac{y}{15}\)

\(\frac{x}{2}=\frac{z}{5}\Rightarrow\frac{x}{8}=\frac{z}{20}\)

Suy ra:  \(\frac{x}{8}=\frac{y}{15}=\frac{z}{20}=\frac{x+y+z}{8+15+20}=\frac{51}{43}\)

Vậy \(x=8.\frac{51}{43}=\frac{408}{43}\)

\(y=15.\frac{51}{43}=\frac{765}{43}\)

\(z=20.\frac{51}{43}=\frac{1020}{43}\)