Question

Tìm 3 số a,b,c:

a/3 bằng 4b/5 ; 10b/3 =5c/2 và a+b+c= 142

Answer 1

\(\frac{a}{3}=\frac{4b}{5}\Rightarrow\frac{a}{3.\frac{3}{10}}=\frac{b}{\frac{5}{4}.\frac{3}{10}}\Rightarrow\frac{a}{\frac{9}{10}}=\frac{b}{\frac{3}{8}}\)

\(\frac{10b}{3}=\frac{5c}{2}\Rightarrow\frac{b}{\frac{3}{10}.\frac{5}{4}}=\frac{c}{\frac{2}{5}.\frac{5}{4}}\Rightarrow\frac{b}{\frac{3}{8}}=\frac{c}{\frac{1}{2}}\)

=> \(\frac{a}{\frac{9}{10}}=\frac{b}{\frac{3}{8}}=\frac{c}{\frac{1}{2}}\)

Áp dụng dãy tỉ số bằng nhau: \(\frac{a}{\frac{9}{10}}=\frac{b}{\frac{3}{8}}=\frac{c}{\frac{1}{2}}=\frac{a+b+c}{\frac{9}{10}+\frac{3}{8}+\frac{1}{2}}=\frac{142}{\frac{71}{40}}=80\)

=> a = 80.9/10=72

b = 80.3/8 =30

c = 80. 1/2 =40