An owner listed a property for 140% more than she paid for it 12 years ago. After receiving no offers during the first three months of market exposure she dropped the list price by 10%, to $172,800. What was the original price that the owner paid for the property?

Let's work through the problem step by step.

Let $ P $ represent the original price the owner paid for the property 12 years ago.

1. The owner initially listed the property at 140% more than the original price, meaning the list price was:
\[
P + 1.4P = 2.4P
\]

2. After receiving no offers, the owner dropped the list price by 10%, so the new price is 90% of the initial list price:
\[
0.9 \times 2.4P = 172,800
\]

3. Simplifying the equation:
\[
2.16P = 172,800
\]

4. Solve for $ P $:
\[
P = \frac{172,800}{2.16} = 80,000
\]

Thus, the original price the owner paid for the property was **$80,000**.

Would you like more details or have any questions?

Here are five related questions:
1. What would the price have been if the owner dropped it by 20% instead of 10%?
2. How much profit would the owner make if the property sold at the reduced price of $172,800?
3. If property values increase by 5% annually, what would be the expected value of this property today based on its original price?
4. How much would the owner have listed the property for if they aimed for a 200% increase instead of 140%?
5. What would the list price have been if the property appreciated at a steady rate over the 12 years?

**Tip**: When solving percentage-based price problems, it's often easier to express everything as a decimal (e.g., 140% as 1.4) to simplify calculations.

Learn how to calculate the original price of a property based on a 140% price increase and a 10% price drop to $172,800. This problem applies percentage-based calculations and algebra, ideal for students in Grades 7-10.

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