Question

If 40% of a number is 10, what is 70% of the number?

Answer 1

well, that number is really "x", which oddly enough is the 100%, now, we also know that 40% of "x" is 10, hmmm

`\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 10& 40 \end{array} \implies \cfrac{x}{10}~~=~~\cfrac{100}{40} \\\\\\ \cfrac{ x }{ 10 } ~~=~~ \cfrac{ 5 }{ 2 }\implies 2x=50\implies x=\cfrac{50}{2}\implies x=25`

hmmm what's 70% of 25 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{70\% of 25}}{\left( \cfrac{70}{100} \right)25}\implies \text{\LARGE 17.5}`