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Chapter 0: Problem 18

Including \(5 \%\) sales tax, an inn charges \(\$ 252\) per night. Find the inn's nightly cost before the tax is added.

Short Answer

Expert verified
The nightly cost before tax is added is \$240.

Step by step solution

01

Understand the tax rate

The problem states that the tax is 5%. Because the total cost includes the tax, the cost before the tax was added can be represented as 100% of the cost. Therefore, the total cost, including the tax, represents 105% (100% original cost + 5% tax) of the pre-tax cost.
02

Calculate the pre-tax cost

To find the pre-tax cost, the total cost ($252) should be divided by 105% (or 1.05 in decimal form). This is because dividing the total cost by the percentage that represents the total cost will yield the original, pre-tax cost.
03

Final Calculation

So the calculation will be as follows: \(\$252 / 1.05 = \$240\)

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