Question

Jim is able to sell a hand-carved statue for $670 which was a 35% profit over his cost. How much did the statue originally cost him?

• A. $496.30
• B. $512.40
• C. $555.40
• D. $574.90
• E. $588.20

Hint:

To reverse a percentage increase (like a profit margin or tax), you divide the final amount by (1 + percentage rate). Don't subtract the percentage from the final amount, as that's a common error.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is another reverse percentage problem, similar to finding the original price after a discount, but this time it involves a profit markup.
Step 2: Key Formula or Approach:
The selling price is the original cost plus the profit. The formula is: \[ \text{Selling Price} = \text{Cost} + (\text{Cost} \times \text{Profit Rate}) = \text{Cost} \times (1 + \text{Profit Rate}) \] To find the original cost, we rearrange the formula: \[ \text{Cost} = \frac{\text{Selling Price}}{1 + \text{Profit Rate}} \] Step 3: Detailed Explanation:
Identify the values from the problem:
Selling Price = $670
Profit Rate = 35% = 0.35
The selling price of $670 represents 100% of the cost plus 35% of the cost, which is 135% of the original cost.
Using the formula: \[ \text{Cost} = \frac{\$670}{1 + 0.35} = \frac{\$670}{1.35} \] \[ \text{Cost} \approx \$496.296296... \] Rounding to the nearest cent (two decimal places): \[ \text{Cost} = \$496.30 \] Step 4: Final Answer:
The statue originally cost Jim approximately $496.30. The correct option is (A).