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

검증된 단계별 안내

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

A 20% reduction means the price is reduced by 20% of $P$, so the sale price is $P - 0.20P = 0.80P$.

We know the sale price after the reduction is $336$, so set up the equation: $0.80P = 336$.

To find the original price $P$, divide both sides of the equation by $0.80$: $P = \frac{336}{0.80}$.

Simplify the right side to find the original price before the reduction.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Percentage Reduction

A percentage reduction represents a decrease in the original amount by a certain percent. For example, a 20% reduction means the new price is 80% of the original price, calculated as 100% - 20% = 80%. Understanding this helps relate the sale price to the original price.

Relationship Between Original and Reduced Price

The reduced price is found by multiplying the original price by the remaining percentage after reduction. If the original price is P and the reduction is r%, then the sale price = P × (1 - r/100). This equation allows solving for the original price when the sale price and reduction are known.

Solving Linear Equations

To find the original price, you set up a linear equation based on the relationship between original and reduced prices. Solving for the unknown involves isolating the variable by performing inverse operations, such as division, to find the original price before the discount.