Question

$\frac{2}{3}$ of a number is 20 less than the original number. Find the number.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{original}\mathrm{number}\mathrm{be}\mathrm{x}. \\ \frac{2}{3}\mathrm{of}\mathrm{the}\mathrm{number}\mathrm{is}20\mathrm{less}\mathrm{than}\mathrm{the}\mathrm{original}\mathrm{number}. \\ \therefore \frac{2}{3}x=x-20 \\ \Rightarrow \frac{2x}{3}=x-20 \\ \Rightarrow 2x=3(x-20)(\mathrm{by}\mathrm{cross}\mathrm{multiplication}) \\ \Rightarrow 2x=3x-60 \\ \Rightarrow 2x-3x=-60 \\ \Rightarrow -x=-60 \\ \Rightarrow x=60 \\ \mathrm{Therefore},\mathrm{the}\mathrm{original}\mathrm{number}\mathrm{is}60. \end{gathered}$$