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Chapter 0: Problem 17

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 inn's nightly cost before tax is \$150

Step by step solution

01

Understand the Problem

We are given that the total cost, including tax, is \$162 and that this total cost represents 108\% of the cost before tax was added. We are to find the original cost before tax was added.
02

Formulate the equation

Let's call the original cost before sales tax as x. We can translate the problem into an equation: \( 1.08x = 162 \). The 1.08 comes from the fact that the cost after adding the 8\% sales tax is 108\% or 1.08 times the original cost.
03

Solve the equation

Rearrange the equation \(1.08x = 162\) to isolate \(x\), the unknown. x is equal to \(162 / 1.08\).
04

Compute the result

Compute \(162 / 1.08 = 150\). So the cost of the inn's nightly stay before tax was added is \$150.

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