A woman saved $225 on the new sofa which was on sale for 30% off. What was the original price of the sofa?
Solve for x to find the original price.
0.3x = 225
750
To find the original price of the sofa, we need to reverse calculate the sale price.
Step 1: Calculate the amount saved
The $225 saved represents a 30% discount on the original price. Let's calculate the amount of discount:
Discount = 30% of original price
= (30/100) * Original price
Amount Saved = Discount
= $225
Step 2: Calculate the original price
To find the original price, we can use the following formula:
Original price = Sale price + Amount saved
Let’s substitute the values we know:
Original price = Sale price + $225
Since the sale price is calculated by taking 30% off the original price, the formula becomes:
Original price = (1 - 30/100) * Original price + $225
Step 3: Simplify the equation
Let’s simplify the equation by multiplying:
Original price = 0.7 * Original price + $225
Step 4: Solve for the original price
Subtract 0.7 * Original price from both sides of the equation:
0.3 * Original price = $225
Divide both sides of the equation by 0.3:
Original price = $225 / 0.3
Step 5: Calculate the original price
Let’s solve the equation:
Original price ≈ $750
Therefore, the original price of the sofa is approximately $750.
To find the original price of the sofa, you need to know the amount saved and the discount rate. In this case, the amount saved is $225 and the discount rate is 30%.
Step 1: Convert the discount rate to a decimal. To do this, divide the discount rate by 100. In this case, 30 ÷ 100 = 0.30.
Step 2: Use the formula: Original Price = Sale Price / (1 - Discount Rate)
Let's calculate:
Original Price = $225 / (1 - 0.30)
Original Price = $225 / 0.70
Original Price = $321.43 (rounded to the nearest cent)
Therefore, the original price of the sofa was approximately $321.43.