Including a 10.5% hotel tax, your room in San Diego cost \$216.58 per night. Find the nightly cost before the tax was added.

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Let the nightly cost before tax be represented by $x$.

The hotel tax is 10.5%, which means the total cost after tax is the original cost plus 10.5% of the original cost. This can be written as $x + 0.105x$.

Combine like terms to express the total cost as \$1.105x$.

Set up the equation $1.105x = 216.58$ to represent the total cost including tax.

Solve for $x$ by dividing both sides of the equation by 1.105: $x = \frac{216.58}{1.105}$.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Percentage and Percent Increase

A percentage represents a part of a whole expressed per hundred. Percent increase involves adding a certain percentage to an original amount, which is essential here to understand how the tax increases the base price.

Finding the Original Amount Before Tax

To find the original price before tax, you divide the total cost by one plus the tax rate expressed as a decimal. This reverses the effect of the added percentage and helps isolate the base price.

Decimal Conversion of Percentages

Percentages must be converted to decimals for calculations by dividing by 100. For example, 10.5% becomes 0.105, which is used in multiplication or division to find amounts related to the percentage.

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