After a 20% reduction, a 42-inch HDTV sold for \$256. What was the price before the reduction?

Verified step by step guidance

1. Understand that the price after a 20% reduction means the HDTV was sold for 80% of its original price, because 100% - 20% = 80%.
2. Let the original price be represented by $P$. The reduced price is then $0.8\; imes\; P$.
3. Set up the equation based on the information given: $0.8\; imes\; P\; =\; 256$.
4. To find the original price $P$, divide both sides of the equation by 0.8: .
5. Simplify the division to express the original price before the reduction.

Key Concepts

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.

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.