Questions: An appliance store decreases the price of a 19-in. television set 28% to a sale price of 459.72. What was the original price? The original price of the television is (Round to the nearest cent.)

An appliance store decreases the price of a 19-in. television set 28% to a sale price of 459.72. What was the original price?

The original price of the television is
(Round to the nearest cent.)

Transcript text: 12 An appliance store decreases the price of a 19 -in. television set $28 \%$ to a sale price of $\$ 459.72$. What was the original price? $\qquad$ The original price of the television is $\$$ $\square$ (Round to the nearest cent.)

Solution

Solution Steps

Step 1: Understand the Problem

We are given the sale price of a television after a 28% discount and need to find the original price. The sale price is $459.72.

Step 2: Set Up the Equation

Let $ x $ be the original price of the television. The television was discounted by 28%, so the sale price is 72% of the original price. We can express this relationship with the equation:

\[ 0.72x = 459.72 \]

Step 3: Solve for the Original Price

To find the original price $ x $, divide both sides of the equation by 0.72:

\[ x = \frac{459.72}{0.72} \]

Step 4: Calculate the Original Price

Perform the division to find $ x $:

\[ x = 638.5 \]

Step 5: Round to the Nearest Cent

Since the problem asks for the original price rounded to the nearest cent, we round $ 638.5 $ to two decimal places:

\[ x = 638.50 \]