Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Equations

College Algebra

1. Equations & Inequalities

Linear Equations

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2:10 minutes

Problem 45

Textbook Question

After a 30% price reduction, you purchase a 50″ 4K UHD TV for $245. What was the television's price before the reduction?

Verified step by step guidance

Let the original price of the TV be denoted as $ x $.

The TV price was reduced by 30%, which means you paid 70% of the original price.

Express the reduced price as an equation: $ 0.7x = 245 $.

To find the original price, solve for $ x $ by dividing both sides of the equation by 0.7.

Calculate $ x = \frac{245}{0.7} $ to find 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

Percentage reduction refers to the decrease in price expressed as a percentage of the original price. In this case, a 30% reduction means that the final price is 70% of the original price. Understanding how to calculate the original price from a reduced price involves recognizing that the final price is a fraction of the original price.

Algebraic Equations

Algebraic equations are mathematical statements that assert the equality of two expressions. To find the original price of the TV, we can set up an equation where the original price multiplied by 70% equals the final price of $245. This requires knowledge of how to manipulate equations to isolate the variable representing the original price.

Solving for a Variable

Solving for a variable involves finding the value of an unknown quantity in an equation. In this scenario, we need to isolate the original price variable by performing inverse operations, such as division, to determine its value. This concept is fundamental in algebra, allowing us to derive unknown values from known quantities.