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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Concetti chiave

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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.

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4:19

Example 2

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.

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Asymptotes of Hyperbolas

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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