Textbook Question
A club with 15 members is to choose four officers–president, vice president, secretary, and treasurer. In how many ways can these offices be filled?
Ch. 8 - Sequences, Induction, and Probability
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 9, Problem 76
After a 20% reduction, a 42-inch HDTV sold for \$256. What was the price before the reduction?
Verified step by step guidance1
Understand that the price after a 20% reduction means the HDTV was sold for 80% of its original price, because 100% - 20% = 80%.
Let the original price be represented by . The reduced price is then .
Set up the equation based on the information given: .
To find the original price , divide both sides of the equation by 0.8: .
Simplify the division to express the original price before the reduction.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Percentage Reduction
A percentage reduction represents a decrease in the original amount by a certain percent. In this problem, a 20% reduction means the final price is 80% of the original price, since 100% - 20% = 80%. Understanding this helps relate the sale price to the original price.
Original Price Calculation
To find the original price before a percentage reduction, divide the reduced price by the remaining percentage expressed as a decimal. For example, if the price after a 20% reduction is $256, the original price is $256 ÷ 0.8. This reverses the effect of the reduction.
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Decimal and Percentage Conversion
Percentages must be converted to decimals for calculations by dividing by 100. For instance, 20% becomes 0.20, and 80% becomes 0.80. This conversion is essential for multiplying or dividing when solving problems involving percentage changes.
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