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

1. Let the original price of the television be represented by the variable \(P\).
2. Since the price was reduced by 30%, the sale price is 70% of the original price. This can be written as the equation: \(0.70 \times P = 245\).
3. To find the original price \(P\), divide both sides of the equation by 0.70: \(P = \frac{245}{0.70}\).
4. Simplify the right side of the equation to express \(P\) in terms of a numerical value (do not calculate the final number).
5. The result from the previous step will give you the original price of the television before the 30% reduction.

Key Concepts

Percentage Decrease

A percentage decrease represents how much a quantity is reduced relative to its original amount, expressed as a percent. In this problem, a 30% price reduction means the new price is 70% of the original price, since 100% - 30% = 70%.

Original Price Calculation

To find the original price before a percentage decrease, divide the reduced price by the remaining percentage (expressed as a decimal). Here, dividing $245 by 0.70 gives the original price before the 30% reduction.

Decimal and Percentage Conversion

Percentages are often converted to decimals for calculations by dividing by 100. For example, 30% becomes 0.30, and 70% becomes 0.70. This conversion is essential for multiplying or dividing when solving percentage problems.