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Keego · Answer 1 · 2023-12-03T21:35:39+0000

$168

Step-by-step explanation:
$\begin{gathered} \text{The cost of \$176.40 per night has the sales tax already included.} \\ We\text{ n}eed\text{ to find the cost per night before the sales tax was added} \end{gathered}$

Let y = sales tax before the tax was added

$\text{Cost after sales tax was added = cost before sales tax was added + cost before sales tax was added(sales tax in \%)}$
$\begin{gathered} \text{sales tax \% = }5\text{ \%} \\ \text{From the formula above:} \\ 176.40\text{ = x + x(}5\text{ \%)} \\ 176.40\text{ = x + x(}0.05\text{)} \\ 176.40\text{ = x + 0}.05x \\ 176.40\text{ = 1}.05x \end{gathered}$
$\begin{gathered} \text{divide both sides by 1.05:} \\ (176.4)/(1.05)\text{ = }(1.05x)/(1.05) \\ x\text{ = }168 \end{gathered}$

Hence, the inn's nightly cost before tax was added is $168

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