Ta có:
20a=7b,8b=5c=>\(\dfrac{a}{7}=\dfrac{b}{20},\dfrac{b}{5}=\dfrac{c}{8}=>\dfrac{a}{7}=\dfrac{b}{20},\dfrac{b}{20}=\dfrac{c}{32}\)=>\(\dfrac{a}{7}=\dfrac{b}{20}=\dfrac{c}{32}\)=>\(\dfrac{2a}{14}=\dfrac{5b}{100}=\dfrac{2c}{64}\)
Áp dụng tính chất dãy tỉ số bằng nhau,ta có:
\(\dfrac{2a}{14}=\dfrac{5b}{100}=\dfrac{2c}{64}=\dfrac{2a+5b-2c}{14+10-64}=\dfrac{100}{50}=2\)
Vậy:
\(\left\{{}\begin{matrix}\dfrac{a}{7}=2\\\dfrac{b}{20}=2\\\dfrac{c}{32}=2\end{matrix}\right.=>\left\{{}\begin{matrix}a=14\\b=40\\c=64\end{matrix}\right.\)
Từ 20a=7b ta có: \(\dfrac{a}{7}=\dfrac{b}{20}\) (1)
Từ 8b = 5c ta có: \(\dfrac{b}{5}=\dfrac{c}{8}\Rightarrow\dfrac{b}{20}=\dfrac{c}{32}\) (2)
Từ (1) và (2) => \(\dfrac{a}{7}=\dfrac{b}{20}=\dfrac{c}{32}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{a}{7}=\dfrac{b}{20}=\dfrac{c}{32}=\dfrac{2a}{14}=\dfrac{5b}{100}=\dfrac{2c}{64}=\dfrac{2a+5b-2c}{14+100-64}=\dfrac{100}{50}=2\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{7}=2\\\dfrac{b}{20}=2\\\dfrac{c}{32}=2\end{matrix}\right.\)
=> a=14; b=40 ; c= 64
