Math Problem Statement

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?

Solution

Let's work through the problem step by step.

Let PP 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=2.4PP + 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: 0.9×2.4P=172,8000.9 \times 2.4P = 172,800

  3. Simplifying the equation: 2.16P=172,8002.16P = 172,800

  4. Solve for PP: P=172,8002.16=80,000P = \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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Percentages

Formulas

List price = Original price + (140% of Original price) = 2.4 × Original price
New price after 10% drop = 0.9 × List price

Theorems

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Suitable Grade Level

Grades 7-10