Textbook Question
In Exercises 1–26, solve and check each linear equation. 3(x - 8) = x
2
views
Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
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 15
After a 20% reduction, you purchase a television for \$336. What was the television's price before the reduction?
Verified step by step guidance1
Let the original price of the television be represented by \(P\).
A 20% reduction means the price is reduced by 20% of \(P\), so the sale price is \(P - 0.20P = 0.80P\).
We know the sale price after the reduction is \(336\), so set up the equation: \(0.80P = 336\).
To find the original price \(P\), divide both sides of the equation by \(0.80\): \(P = \frac{336}{0.80}\).
Simplify the right side to find the original price before the reduction.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2mWas this helpful?
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. For example, a 20% reduction means the new price is 80% of the original price, calculated as 100% - 20% = 80%. Understanding this helps relate the sale price to the original price.
Relationship Between Original and Reduced Price
The reduced price is found by multiplying the original price by the remaining percentage after reduction. If the original price is P and the reduction is r%, then the sale price = P × (1 - r/100). This equation allows solving for the original price when the sale price and reduction are known.
Recommended video:
3:58
Graphing Hyperbolas at the Origin Example 1
Solving Linear Equations
To find the original price, you set up a linear equation based on the relationship between original and reduced prices. Solving for the unknown involves isolating the variable by performing inverse operations, such as division, to find the original price before the discount.
Recommended video:
04:02Solving Linear Equations with Fractions
Related Practice
Textbook Question
Solve each equation in Exercises 15–34 by the square root property.
4
views
Textbook Question
In Exercises 15–26, use graphs to find each set. (- 3, 0) ∩ [- 1, 2]
Textbook Question
Find each product and write the result in standard form. (3 + 5i)(3 - 5i)
1
views
Textbook Question
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x-5 = 7
Textbook Question
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = x - 2
1
views