Question

Including a 6% sales tax, an inn charges $155.82 per night. Find the inn's nightly cost before tax is added.

Answer 1

we know the Inn is charging 155.82 and that's 100% plus 6%, namely 106% of an amout of say that is "x", being the 100%.

since we know that 155.82 is 106%, what is "x"?

`\begin{array}{ccll} amount&\%\\ \cline{1-2} 155.82&106\\ x&100 \end{array}\implies \cfrac{155.82}{x}=\cfrac{106}{100}\implies \cfrac{155.82}{x}=\cfrac{53}{50} \\\\\\ 7791=53x\implies \cfrac{7791}{53}=x\implies 147=x`