Vì 5a=8b=20c
\(\dfrac{\Rightarrow5a}{120}=\dfrac{8b}{120}=\dfrac{20c}{120}\)
\(\dfrac{\Rightarrow a}{24}=\dfrac{b}{15}=\dfrac{c}{6}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{a}{24}=\dfrac{b}{15}=\dfrac{c}{6}=\dfrac{\left(a-b-c\right)}{24-15-6}=\dfrac{3}{3}=1\)
\(\Rightarrow\left\{{}\begin{matrix}a=24\\b=15\\c=6\end{matrix}\right.\)
vi 5a=8b=20c
=> 5a=8b
=> 8b=20c
5a=8b=> \(\dfrac{a}{8}\)=\(\dfrac{b}{5}\)=> \(\dfrac{a}{32}\)=\(\dfrac{b}{20}\)
8b=20c => \(\dfrac{b}{20}\)=\(\dfrac{c}{8}\)
==> \(\dfrac{a}{32}\)=\(\dfrac{b}{20}\)=\(\dfrac{c}{8}\)và a-b-c=3
áp dụng tính chất dãy tỉ số bằng nhau ta có
\(\dfrac{a}{32}\)=\(\dfrac{b}{20}\)=\(\dfrac{c}{8}\)=\(\dfrac{a-b-c}{32-20-8}\)=\(\dfrac{3}{4}\)
vì \(\dfrac{a}{32}\)=\(\dfrac{3}{4}\)=>a= \(\dfrac{3}{4}\).32=24
\(\dfrac{b}{20}\)=\(\dfrac{3}{4}\)=> b= \(\dfrac{3}{4}\).20=15
\(\dfrac{c}{8}\)=\(\dfrac{3}{4}\)=> c= \(\dfrac{3}{4}\).8=6
vậy a= 24
b=15
c=6
