Questlons Luke buys a television that is on sale for \( 25 \% \) off the original price. The original price is \( \$ 120 \) more than the sale price. What is the original price of the televisio

Let's solve the problem step by step. **Given:** - The television is on sale for **25% off** the original price. - The **original price** is **\$120 more** than the sale price. **Let’s define:** - \( P \) = Original price of the television **Step 1: Express the Sale Price in Terms of the Original Price** A 25% discount means the sale price is 75% of the original price. \[ \text{Sale Price} = P - 0.25P = 0.75P \] **Step 2: Set Up the Equation Based on the Given Information** According to the problem, the original price is \$120 more than the sale price. \[ P = \text{Sale Price} + 120 \\ P = 0.75P + 120 \] **Step 3: Solve for \( P \)** First, subtract \( 0.75P \) from both sides to isolate terms involving \( P \): \[ P - 0.75P = 120 \\ 0.25P = 120 \] Next, divide both sides by 0.25 to find \( P \): \[ P = \frac{120}{0.25} \\ P = 480 \] **Answer:** The **original price** of the television is **\$480**.