Question

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

Tìm a,b,c

Answer 1

\(\dfrac{1}{2}a=\dfrac{2}{3}b=\dfrac{3}{4}c\\ \dfrac{a}{2}=\dfrac{2b}{3}\\ \Rightarrow3a=2\cdot2b\\ \Leftrightarrow3a=4b\\ \Rightarrow\dfrac{a}{4}=\dfrac{b}{3}\left(\text{tỉ lệ thức}\right)\)

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

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

\(\dfrac{a}{4}=15\Rightarrow a=15\cdot4=60\\ \dfrac{b}{3}=15\Rightarrow b=15\cdot3=45\)

Thay vào ta có:

\(\dfrac{1}{2}a=\dfrac{2}{3}b=\dfrac{3}{4}c\\ \Leftrightarrow\dfrac{1}{2}\cdot60=\dfrac{2}{3}\cdot45=\dfrac{3}{4}c\\ \Leftrightarrow30=30=\dfrac{3}{4}c\\ \Rightarrow\dfrac{3}{4}c=30\\ c=30:\dfrac{3}{4}\\ c=40\)

Vậy \(a=60,b=45,c=40\)