\(\frac{2a}{3}=\frac{3b}{4}=\frac{4c}{5}\) hay \(\frac{a}{\frac{3}{2}}=\frac{b}{\frac{4}{3}}=\frac{c}{\frac{5}{4}}\)
Áp dụng t/c dãy tỉ số bằng nhau,ta có: \(\frac{a}{\frac{3}{2}}=\frac{b}{\frac{4}{3}}=\frac{c}{\frac{5}{4}}=\frac{a+b+c}{\frac{3}{2}+\frac{4}{3}+\frac{5}{4}}=\frac{49}{\frac{49}{12}}=12\)
Suy ra \(a=12.\frac{3}{2}=18\);\(b=12.\frac{4}{3}=16\); \(c=12.\frac{5}{4}=15\)
Vậy ...
Ta có : \(\frac{2a}{3}=\frac{3b}{4}=\frac{4c}{5}\)
\(\Rightarrow\frac{12a}{18}=\frac{12b}{16}=\frac{12c}{15}=k\)
Áp dụng tính chất dãy tỉ số bằng nhau :
\(k=\frac{12a+12b+12c}{18+16+15}=\frac{12\left(a+b+c\right)}{49}\) \(=\frac{12.49}{49}=12\) ( vì \(a+b+c=49\))
Do đó : \(\frac{2a}{3}=12\Rightarrow2a=36\Rightarrow a=18\)
\(\frac{3b}{4}=12\Rightarrow3b=48\Rightarrow b=16\)
\(\Rightarrow\frac{4c}{5}=12\Rightarrow4c=60\Rightarrow c=15\)
Vậy \(a=18;b=16;c=15\)