Problem 36
Question
Including \(5 \%\) sales tax, an inn charges \(\$ 252\) per night. Find the inn's nightly cost before the tax is added.
Step-by-Step Solution
Verified Answer
The inn's nightly cost before the tax is added is approximately $240.
1Step 1: Understand the problem
Recognize that the total cost is made up of the original cost plus the 5% sales tax. This makes the total 105% of the original cost.
2Step 2: Formulate the equation
Formulate an equation that represents the final cost as 105% of the original cost: \(1.05 \times\) (original cost) = $252.
3Step 3: Solve for the original cost
Isolate the original cost by dividing $252 by \(1.05\). This will give us the original cost before the tax was added.
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