Question

Cho a:b = 9:4 và b: c= 5: 3 . Tìm tỉ số ( a-b ) : (b-c )

giải cụ thể nha

Answer 1

Từ \(a:b=9:4\Rightarrow\dfrac{a}{b}=\dfrac{9}{4}\Rightarrow\dfrac{a}{9}=\dfrac{b}{4}\Rightarrow\dfrac{a}{45}=\dfrac{b}{20}\)

Và \(b:c=5:3\Rightarrow\dfrac{b}{c}=\dfrac{5}{3}\Rightarrow\dfrac{b}{5}=\dfrac{c}{3}\Rightarrow\dfrac{b}{20}=\dfrac{c}{12}\)

\(\Rightarrow\dfrac{a}{45}=\dfrac{b}{20};\dfrac{b}{20}=\dfrac{c}{12}\Rightarrow\dfrac{a}{45}=\dfrac{b}{20}=\dfrac{c}{12}\)

Đặt \(\dfrac{a}{45}=\dfrac{b}{20}=\dfrac{c}{12}=k\Rightarrow a=45k;b=20k;c=12k\)

Khi đó \(A=\dfrac{a-b}{b-c}=\dfrac{45k-20k}{20k-12k}=\dfrac{25k}{8k}=\dfrac{25}{8}\)

Answer 2

Ta có: \(\dfrac{a}{b}=\dfrac{9}{4}\Rightarrow\dfrac{a}{9}=\dfrac{b}{4}\Rightarrow\dfrac{a}{45}=\dfrac{b}{20}\)

\(\dfrac{b}{c}=\dfrac{5}{3}\Rightarrow\dfrac{b}{5}=\dfrac{c}{3}\Rightarrow\dfrac{b}{20}=\dfrac{c}{12}\)

Xét: \(\dfrac{a}{45}=\dfrac{b}{20}=\dfrac{c}{12}=k\Rightarrow\left\{{}\begin{matrix}a=45k\\b=20k\\c=12k\end{matrix}\right.\)

Thay \(\left\{{}\begin{matrix}a=45k\\b=20k\\c=12k\end{matrix}\right.\) vào \(\dfrac{a-b}{b-c}\)

Ta được: \(\dfrac{45k-20k}{20k-12k}=\dfrac{\left(45-20\right)k}{\left(20-12\right)k}=\dfrac{25k}{8k}=\dfrac{25}{8}\)

Vậy: .........................................