Question

a women earns 16% more than her husband. Together they make 72,360 per year. what is the husbands annual salary

Answer 1

well, her husband makes "x" in salary, hmmm hers is 16% more than that, so

`\begin{array}ll \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{16\% of x}}{\left( \cfrac{16}{100} \right)x}\implies 0.16x`

so she really makes x + 0.16x = 1.16x, and we know their total is 72,360, so

`\stackrel{husband}{x} + \stackrel{hers}{1.16x} = 72360\implies 2.16x=72360\implies x=\cfrac{72360}{2.16}\implies \boxed{x = 33500}`