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Chapter 6: Problem 39

Including \(8 \%\) sales tax, an inn charges \(\$ 162\) per night. Find the inn's nightly cost before the tax is added.

Short Answer

Expert verified
The cost of the inn's nightly stay before tax is $150.

Step by step solution

01

Identify the given variables

The problem gives the final amount which is $162. This amount includes a sales tax of 8%. We need to find the initial price (before tax). Thus, the final amount = $162 and the tax rate = 8% or 0.08 in decimal.
02

Apply the formula for the original amount before tax.

The formula for calculating the original amount before tax is: \(Original Amount = Final amount / (1 + Tax Rate)\). Substituting the given numbers into this formula gives \(Original Amount = 162 / (1+0.08)\).
03

Perform calculations to find the original amount

By performing the division, we find that the original amount is approximately $150.
04

Verify the result

To verify that our result is correct, we can add 8% of $150 to itself. This results in \(150 + (0.08*150) = 162\), further confirming our solution.

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