Question

Tìm a,b,c biết:

\(\dfrac{1}{2}a=\dfrac{2}{3}b=\dfrac{3}{4}c\) và a - b= 15

Answer 1

\(\dfrac{1}{2}a=\dfrac{2}{3}b=\dfrac{3}{4}c\Leftrightarrow\dfrac{a}{2}=\dfrac{2b}{3}=\dfrac{3c}{4}\)
\(\Rightarrow\dfrac{a}{2}.\dfrac{1}{6}=\dfrac{2b}{3}.\dfrac{1}{6}=\dfrac{3c}{4}.\dfrac{1}{6}\)

\(\Rightarrow\dfrac{a}{12}=\dfrac{2b}{18}=\dfrac{3c}{24}\)

\(\Rightarrow\dfrac{a}{12}=\dfrac{b}{9}=\dfrac{c}{8}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{a}{12}=\dfrac{b}{9}=\dfrac{c}{8}=\dfrac{a-b}{12-9}=\dfrac{15}{3}=5\)

\(\Rightarrow\left\{{}\begin{matrix}a=60\\b=45\\c=40\end{matrix}\right.\)