Including a 17.4% hotel tax, your room in Chicago cost \$287.63 per night. Find the nightly cost before the tax was added.

검증된 단계별 안내

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

The hotel tax is 17.4%, which can be written as a decimal: $0.174$.

The total cost after adding the tax is the original cost plus 17.4% of the original cost, which can be expressed as $x + 0.174x$ or equivalently \$1.174x$.

Set up the equation representing the total cost including tax: $1.174x = 287.63$.

Solve for $x$ by dividing both sides of the equation by $1.174$: $x = \frac{287.63}{1.174}$.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Percentage and Percent Increase

A percentage represents a part of a whole expressed per hundred. Percent increase refers to how much a quantity grows relative to its original amount, often calculated by adding a certain percent to the original value. In this problem, the hotel tax is a 17.4% increase on 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 percentage increase, isolating the base price before the tax was added.

Converting Percent to Decimal

Percent values must be converted to decimals for calculations by dividing by 100. For example, 17.4% becomes 0.174. This conversion is essential for multiplying or dividing when working with percentages in algebraic problems.