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Chapter 6: Problem 40

Including \(5 \%\) sales tax, an inn charges \(\$ 252\) per night. Find the inn's nightly cost before the tax is added.

Short Answer

Expert verified
The nightly cost of the inn before tax is approximately \$ 240.

Step by step solution

01

Understand the Situation

The price charged per night is $252. This price includes a 5% tax. The goal is to find out the price before the tax was added.
02

Create an Equation

Let x be the price before tax. You are given that the total price is \(x + 0.05x = 252\), which includes 5% tax.
03

Simplify the Equation

Combine like terms to simplify the equation. This becomes \(1.05x = 252\). The equation just says that 105% of the original price is equal to $252.
04

Solve for x

Divide both sides of the equation by 1.05 to find the value of x, which represents the price before tax is added. So \(x = 252/1.05\).
05

Find the Price Before Tax

Carry out the calculation to find the original price before tax was added. This will provide the price per night before the tax was added.

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