Textbook Question
Solve each equation in Exercises 15–34 by the square root property. 3x2 - 1 = 47
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 2, Problem 19
Exercises 19–20 involve markup, the amount added to the dealer's cost of an item to arrive at the selling price of that item. The selling price of a refrigerator is \$1198. If the markup is 25% of the dealer's cost, what is the dealer's cost of the refrigerator?
Verified step by step guidance1
Let the dealer's cost be represented by the variable \(C\).
Since the markup is 25% of the dealer's cost, the markup amount can be expressed as \(0.25 \times C\).
The selling price is the sum of the dealer's cost and the markup, so we write the equation: \(C + 0.25 \times C = 1198\).
Combine like terms on the left side to get \(1.25 \times C = 1198\).
Solve for \(C\) by dividing both sides of the equation by 1.25: \(C = \frac{1198}{1.25}\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Markup Percentage
Markup percentage is the rate at which the dealer increases the cost price to determine the selling price. It is usually expressed as a percentage of the dealer's cost. In this problem, the markup is 25%, meaning the selling price is the cost plus 25% of the cost.
Relationship Between Cost, Markup, and Selling Price
The selling price is calculated by adding the markup to the dealer's cost. Mathematically, Selling Price = Cost + Markup. Since markup is a percentage of cost, this can be written as Selling Price = Cost × (1 + Markup Rate). This relationship helps to find the unknown cost when selling price and markup rate are known.
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Solving Linear Equations
To find the dealer's cost, you set up an equation based on the relationship Selling Price = Cost × (1 + Markup Rate) and solve for the cost. This involves isolating the variable by dividing both sides of the equation by (1 + Markup Rate), which is a basic algebraic technique for solving linear equations.
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