Ch. 1 - Equations and Inequalities

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 1 - Equations and Inequalities

Problem 18

Chapter 2, Problem 18

Including a 17.4% hotel tax, your room in Chicago cost \$287.63 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 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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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 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.

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