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 TV be denoted as \( x \).
2. The TV price was reduced by 30%, which means you paid 70% of the original price.
3. Express the reduced price as an equation: \( 0.7x = 245 \).
4. To find the original price, solve for \( x \) by dividing both sides of the equation by 0.7.
5. Calculate \( x = \frac{245}{0.7} \) to find the original price before the reduction.

Key Concepts

Percentage Reduction

Percentage reduction refers to the decrease in price expressed as a percentage of the original price. In this case, a 30% reduction means that the final price is 70% of the original price. Understanding how to calculate the original price from a reduced price involves recognizing that the final price is a fraction of the original price.

Algebraic Equations

Algebraic equations are mathematical statements that assert the equality of two expressions. To find the original price of the TV, we can set up an equation where the original price multiplied by 70% equals the final price of $245. This requires knowledge of how to manipulate equations to isolate the variable representing the original price.

Solving for a Variable

Solving for a variable involves finding the value of an unknown quantity in an equation. In this scenario, we need to isolate the original price variable by performing inverse operations, such as division, to determine its value. This concept is fundamental in algebra, allowing us to derive unknown values from known quantities.