Question

If 20% of x is equal to x-20, what is the value of x?

Answer 1

well, first off, what's 20% of "x" anyway?

`\begin{array} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{20\% of x}}{\left( \cfrac{20}{100} \right)x}\implies \cfrac{20x}{100}\implies \cfrac{x}{5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x}{5}~~ = ~~x-20\implies x=5x-100\implies x+100=5x \\\\\\ 100=4x\implies \cfrac{100}{4}=x\implies \boxed{20=x}`