Question

a brokerage firm charges 1 1/4% if its fee on stock purchase was 400$ what was amount of purchase?​

Answer 1

let's say the amount purchased was "x", so then that's the 100%.

if we know that 400 is the 1¼% and "x" is the 100%, what is "x"?

$\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 400&1\frac{1}{4} \end{array}\implies \cfrac{x}{400}=\cfrac{100}{1\frac{1}{4}}\implies \cfrac{x}{400}=\cfrac{100}{\frac{1\cdot 4+1}{4}}\implies \cfrac{x}{400}=\cfrac{\frac{100}{1}}{\frac{5}{4}} \\\\\\ \cfrac{x}{400}=\cfrac{\stackrel{20}{~~\begin{matrix} 100 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{1}\cdot \cfrac{4}{~~\begin{matrix} 5 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x}{400}=80\implies x=32000$