Question

Tìm x thỏa mãn:

\(\frac{1+3y}{12}=\frac{1+6y}{16}=\frac{1+9y}{4x}\)

Answer 1

\(\frac{1+3y}{12}=\frac{1+6y}{16}=\frac{1+9y}{4x}\)

\(\Leftrightarrow12\left(1+6y\right)=16\left(1+3y\right)\)

\(\Leftrightarrow3\left(1+6y\right)=4\left(1+3y\right)\)

\(\Leftrightarrow3+18y=4+12y\)

\(\Leftrightarrow3-4=12y-18y\)

\(\Leftrightarrow-1=-6y\)

\(\Rightarrow y=\frac{1}{6}\)

\(\Rightarrow\frac{1+3y}{12}=\frac{1+3.\frac{1}{6}}{12}=\frac{1+9.\frac{1}{6}}{4x}\)

\(\Leftrightarrow\frac{\frac{3}{2}}{12}=\frac{\frac{5}{2}}{4x}\)

\(\Leftrightarrow\frac{1}{8}=\frac{\frac{5}{2}}{4x}\)

\(\Rightarrow4x=8.\frac{5}{2}=20\)

\(\Rightarrow x=20:4=5\)

Vậy \(x=5\)