The price of the room at the inn before taxes are added is $160.
Work Step by Step
First, we need to define our unknown. What we want to find out how much the inn charges per night before taxes are added. We will designate this unknown as $x$. We will need to add the amount of the tax to the price of the room before taxes to get the final price of $172.80$ dollars. The tax is $8$%, so the amount of taxes added to the price of the room rental can be given by the expression (8%)$(x)$. We cannot work with percentages, so we change the percent into a decimal. We do this by dividing the percentage by $100$ to get rid of the percentage sign. We now have the percentage changed to the decimal $0.08$. We can now set up the following equation to find the price of the room at the inn before the sales tax was added: $$x + 0.08x = 172.80$$ We combine like terms: $$1.08x = 172.80$$ To solve for $x$, we divide both sides of the equation by $1.08$: $$x = 160$$ The price of the room at the inn before taxes are added is $160.