Question

The sales price of a car is $12,590, which is 20% off the original price. What is the original price?

• A. $14,310.40
• B. $14,990.90
• C. $15,290.70
• D. $15,737.50
• E. $16,935.80

Hint:

A common mistake is to add 20% of the sales price back to it. This is incorrect. To reverse a percentage decrease, you must divide by (1 - percentage rate), not multiply.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This is a reverse percentage problem. We are given the final price after a discount and need to find the original price.
Step 2: Key Formula or Approach:
If the sales price is the result of a discount, the relationship is: \[ \text{Sales Price} = \text{Original Price} \times (1 - \text{Discount Rate}) \] To find the original price, we rearrange the formula: \[ \text{Original Price} = \frac{\text{Sales Price}}{1 - \text{Discount Rate}} \] Step 3: Detailed Explanation:
The sales price is $12,590.
The discount rate is 20% or 0.20.
This means the sales price represents \( 100% - 20% = 80% \) of the original price.
Using the formula: \[ \text{Original Price} = \frac{\$12,590}{1 - 0.20} = \frac{\$12,590}{0.80} \] \[ \text{Original Price} = \$15,737.50 \] Step 4: Final Answer:
The original price of the car was $15,737.50. The correct option is (D).