After a 20% reduction, you purchase a television for $336. What was the television's price before the reduction?

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Let the original price of the television be $ x $.

The television was reduced by 20%, which means you paid 80% of the original price.

Express the reduced price as an equation: $ 0.8x = 336 $.

To find the original price $ x $, divide both sides of the equation by 0.8.

Solve for $ x $ to find the original price of the television.

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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 value expressed as a percentage of the original price. In this case, a 20% reduction means that the price of the television was lowered by 20% of its original price. Understanding how to calculate percentage reductions is essential for determining the original price from the sale price.

Finding the Original Price

To find the original price after a percentage reduction, you can use the formula: Original Price = Sale Price / (1 - Percentage Reduction). Here, the sale price is $336, and the percentage reduction is 20%, or 0.20 in decimal form. This formula allows you to reverse the reduction and find the initial price before the discount.

Basic Algebraic Manipulation

Basic algebraic manipulation involves rearranging equations to isolate variables. In this context, you need to manipulate the equation to solve for the original price. This skill is fundamental in algebra, as it allows you to work with equations and find unknown values effectively.

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