Textbook Question
Simplify and write the result in standard form. √-108
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 32
A repair bill on a sailboat came to \$2356, including \$826 for parts and the remainder for labor. If the cost of labor is \$90 per hour, how many hours of labor did it take to repair the sailboat?
Verified step by step guidance1
Identify the total cost of the repair bill, which is \$2356, and the cost of parts, which is \$826.
Calculate the cost of labor by subtracting the cost of parts from the total bill: \(2356 - \)826 = \(\text{labor cost}\)$.
Let the number of labor hours be represented by \(h\). Since labor costs \$90 per hour, the total labor cost can be expressed as \$90h$.
Set up the equation for labor cost: \(90h = \text{labor cost}\) (from step 2).
Solve for \(h\) by dividing both sides of the equation by 90: \(h = \frac{\text{labor cost}}{90}\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Understanding Total Cost Breakdown
The total cost is composed of parts and labor costs. To find the labor cost, subtract the cost of parts from the total bill. This step isolates the amount spent specifically on labor.
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Solving Linear Equations
Once the labor cost is known, use a simple linear equation to find the number of labor hours. Divide the labor cost by the hourly rate to solve for the unknown variable representing hours worked.
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Unit Rate and Division
The hourly labor rate is a unit rate, meaning cost per one hour. Dividing the total labor cost by this unit rate converts total cost into total hours, linking monetary values to time.
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Related Practice
Textbook Question
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 8x - 11 ≤ 3x - 13
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Textbook Question
Solve each equation in Exercises 15–34 by the square root property. (8x - 3)2 = 5
Textbook Question
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 = 2x/3 + 1
Textbook Question
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. -9x ≥ 36
Textbook Question
Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)3/2 = 27