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Chapter 0: Problem 18

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 inn's nightly cost before tax is approximately \$240.

Step by step solution

01

Interpret the problem

Understand that the final cost of the inn's nightly charge (\$252) is made up of 100% of the original cost plus 5% sales tax. This means \$252 is equal to 105% of the original cost.
02

Write the equation

Set up the equation based on the problem. Let \(X\) be the original cost. Then the equation would be \(1.05X = \$252\).
03

Solve for X

To solve for \(X\), divide both sides of the equation by 1.05: \(X = \$252 / 1.05\).
04

Perform the computation

When you perform the division, you get that \(X \approx \$240\). This is the inn's nightly cost before the tax is added.

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