Problem 15 - Algebra and Trigonometry

Question

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

Step-by-Step Solution

Answer

Using the equation derived and calculated in Step 3, the Original Price of the television before the reduction is \$420.

Step 1: Identify the reduction and the post-reduction price

The television was reduced by 20% and then purchased for \$336. It needs to be understood that \$336 represents 80% of the original price, since 100% - 20% = 80%.

Step 2: Set up the equation

From Step 1, it is known that 80% of the original price equals \$336. This can be represented as an equation: \(0.8 \times \text{Original Price} = \$336\).

Step 3: Solve for the Original Price

To find the Original Price, divide both sides of the equation by 0.8. \( \text{Original Price} = \frac{\$336}{0.8}\)