Math CentralQuandaries & Queries


Question from mike:

What is the percent difference between two homes if one is worth $525,000 and the other is $425,000. (525,000 - 425,000 = 100,000)

Hi Mike,

We tend to be inexact when we use the term percent. We should always say "percent of what". A shopkeeper might advertise "15% off" and what is meant is that the price is reduced by 15% of the usual price. My house taxes have increased 7% over last year. Here I mean that the increase in my taxes is 7% of last year's taxes. Often, as in the house taxes example a quantity has changed from an original value to a new value and we talk about percentage change. In this case what is usually meant is the change as a percentage of the original value. Thus using your numbers if a house sold for $425,00 five years ago and then sold this year for $525,000 then the percentage change is ($525,000 - $425,000)/$425,000 × 100 = $100,000/$425,000 × 100 = 23.5%. A 24% increase. If the house sold for $525,000 five years ago and then $425 this year then the percentage change is ($425,000 - $525,000)/$525,000 × 100 = -$100,000/$525,000 × 100 = -19.0%. A 19% decrease.

Since you asked for percent difference and didn't indicate percent of what I don't know how to answer in a way that another reader would know what you have done.


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