Question

Including a 5% sales tax, an inn charges $189 per night. Find the inn's nightly cost before tax is added.

a) $180
b) $179.55
c) $198.45
d) $184

Answer 1

The inn's nightly cost before the 5% sales tax is added is $180, found by dividing the total cost of $189 by 1.05.

Step-by-step explanation:

To find the inn's nightly cost before tax is added, we need to work backward from the total cost including tax. The total cost given is $189 which includes the base price of the inn's nightly cost plus a 5% sales tax. First, we need to convert the percent to a decimal by dividing by 100, which makes 5% equal to 0.05. The equation representing the total cost including tax is: base cost + (base cost * tax rate) = total cost. In this case, the tax rate is 0.05.

To isolate the base cost, we divide the total cost by (1 + tax rate), which gives us base cost = $189 / (1 + 0.05). Plugging the numbers in, we get base cost = $189 / 1.05. Calculating this, we find the base cost is $180. Therefore, the inn's nightly cost before tax is $180, which corresponds to option a).