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Chapter 1: Problem 35

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 nightly cost before tax is approximately $150.

Step by step solution

01

Understand the percentages

We have the total amount that includes 8% tax. This means, the final price is 108% of the initial price. Let's denote the initial price (the price before tax) as \(P\). Then, we can say that \(108\% \) of \(P\) equals $162.
02

Setting up the equation

Based on the relation established in the previous step, set up the equation: \(1.08 \cdot P = 162\), where 1.08 is the numerical value of 108% (since 1 corresponds to 100% and 0.08 corresponds to 8%).
03

Solving for P

To find \(P\) (the initial price), divide both sides of the equation by 1.08: \(P = 162/1.08\). Calculate this to find the value of \(P\).

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