Math Problem Statement

A house was originally listed for sale at $250,000. After 3 months, the seller dropped the price to $200,000. What was the percent of change in the price?

Solution

To find the percent change in the price of the house, you can use the formula for percent change:

Percent Change=Old PriceNew PriceOld Price×100\text{Percent Change} = \frac{\text{Old Price} - \text{New Price}}{\text{Old Price}} \times 100

Given:

  • Old Price = $250,000
  • New Price = $200,000

Now, plug the values into the formula:

Percent Change=250,000200,000250,000×100\text{Percent Change} = \frac{250,000 - 200,000}{250,000} \times 100

Percent Change=50,000250,000×100\text{Percent Change} = \frac{50,000}{250,000} \times 100

Percent Change=0.2×100=20%\text{Percent Change} = 0.2 \times 100 = 20\%

So, the percent decrease in the price is 20%.

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

  1. How would the percentage change if the price dropped to $180,000?
  2. What if the seller had increased the price instead—how would you calculate the percent increase?
  3. If the house was later sold at $220,000, what would be the percent change from the original price?
  4. How would the formula change if dealing with an increase rather than a decrease?
  5. How can you determine the final price if given a percent change and the original price?

Tip: When calculating percent change, always make sure to subtract the new value from the old one for a decrease, and reverse it for an increase!

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Math Problem Analysis

Mathematical Concepts

Percentage
Percent Change
Basic Arithmetic

Formulas

Percent Change = (Old Price - New Price) / Old Price * 100

Theorems

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Suitable Grade Level

Grades 6-8