Question

Kylie buys a ceramic case priced at $75. Shipping and handling are an additional 9 2/5% of the price. How much shopping and handling will Kylie pay?

Answer 1

$\bf \begin{array}{ccllll} amount&\%\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 75&100\\ x&9\frac{2}{5} \end{array}\implies \cfrac{75}{x}=\cfrac{100}{9\frac{2}{5}}\implies \cfrac{75}{x}=\cfrac{100}{\frac{9\cdot 5+2}{5}}$

$\bf \cfrac{75}{x}=\cfrac{\frac{100}{1}}{\frac{47}{5}}\implies \cfrac{75}{x}=\cfrac{100}{1}\cdot \cfrac{5}{47}\implies \cfrac{75}{x}=\cfrac{500}{47}\implies 75\cdot 47=500\cdot x \\\\\\ \cfrac{3525}{500}=x\implies \cfrac{141}{20}=x\implies 7.05=x$