Question

[Phạm Trà Giang]

Tìm x, y biết:

\(\frac{1+2013x}{60}=\frac{1+2015x}{5y}=\frac{1+2017x}{4y}\)

Answer 1

[~_~ ^~^ ^_^ {_} +_+ -_- ?_?....]

mấy thánh

Answer 2

[Chu Công Đức]

Ta có: \(\frac{1+2013x}{60}=\frac{1+2017x}{4y}=\frac{1+2013x+1+2017x}{60+4y}=\frac{2+4030x}{60+4y}\)  

\(=\frac{2\left(1+2015x\right)}{2\left(30+2y\right)}=\frac{1+2015x}{30+2y}\)

mà \(\frac{1+2013x}{60}=\frac{1+2015x}{5y}=\frac{1+2017x}{4y}\)\(\Rightarrow\frac{1+2015x}{5y}=\frac{1+2015x}{30+2y}\)

\(\Rightarrow5y=30+2y\)\(\Leftrightarrow5y-2y=30\)\(\Leftrightarrow3y=30\)\(\Leftrightarrow y=10\)

Thay \(y=10\)vào biểu thức ta được:\(\frac{1+2013x}{60}=\frac{1+2015x}{5.10}=\frac{1+2015x}{50}\)

\(\Rightarrow50\left(1+2013x\right)=60\left(1+2015x\right)\)

\(\Leftrightarrow50+100650x=60+120900x\)\(\Leftrightarrow120900x-100650x=50-60\)

\(\Leftrightarrow20250=-10\)\(\Leftrightarrow x=\frac{-10}{20250}=\frac{-1}{2025}\)

Vậy \(x=\frac{-1}{2025}\)và \(y=10\)