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

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Let the original price of the television be represented by the variable $P$.

Since the price was reduced by 30%, the sale price is 70% of the original price. This can be written as the equation: $0.70 \times P = 245$.

To find the original price $P$, divide both sides of the equation by 0.70: $P = \frac{245}{0.70}$.

Simplify the right side of the equation to express $P$ in terms of a numerical value (do not calculate the final number).

The result from the previous step will give you the original price of the television before the 30% reduction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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