Percents Of Percents Of Percents

It's always easier to convert all the percentages to fractions, which is easier to work with. We have

$25\% = \dfrac{25}{100} = \dfrac14, \quad x\% = \dfrac{x}{100}$

By converting the phrase: 25% of $x\%$ of $x\%$ of $x$ is 18.225 into a mathematical expression, we have

$\begin{aligned} 25\% \cdot x\% \cdot x\% \cdot x & = & 18.225 \\ \dfrac14 \cdot \dfrac x{100} \cdot \dfrac x{100} \cdot x &=& 18.225 \\ \dfrac {x^3}{4 \cdot 100^2} &=& 18.225 \\ x^3& = &4 \cdot 100^2 \cdot 18.225 \\ & = & 729000 \\ x & = & \sqrt[3]{729000} =\boxed{90} \end{aligned}$

Wrong solution!!! 4 . 100 . 18225 = 729 000 000 so X = 900