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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 inn's nightly cost before the tax is added is \$150.

Step by step solution

01

Identify the variables

Let's denote the original price of the inn's nightly cost as \( X \). The price after tax is \(\$162\), and the rate of sales tax is \(8\%\).
02

Apply the percentage increase formula

Since the final price \(\$162\) is the result of a \(8\%\) increase to the original price, it can be written as \(X + 0.08*X = 162\).
03

Simplify the equation and solve for X

When you add like terms this equation simplifies to \(1.08X = 162\). Solve for \(X\) by dividing both sides by \(1.08\). So, \(X = 162 / 1.08 = 150\).

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