$168
Explanation:[tex]\begin{gathered} \text{The cost of \$176.40 per night has the sales tax already included.} \\ We\text{ n}eed\text{ to find the cost per night before the sales tax was added} \end{gathered}[/tex]
Let y = sales tax before the tax was added
[tex]\text{Cost after sales tax was added = cost before sales tax was added + cost before sales tax was added(sales tax in \%)}[/tex][tex]\begin{gathered} \text{sales tax \% = }5\text{ \%} \\ \text{From the formula above:} \\ 176.40\text{ = x + x(}5\text{ \%)} \\ 176.40\text{ = x + x(}0.05\text{)} \\ 176.40\text{ = x + 0}.05x \\ 176.40\text{ = 1}.05x \end{gathered}[/tex][tex]\begin{gathered} \text{divide both sides by 1.05:} \\ \frac{176.4}{1.05}\text{ = }\frac{1.05x}{1.05} \\ x\text{ = }168 \end{gathered}[/tex]
Hence, the inn's nightly cost before tax was added is $168
