# Percentage expensive or cheaper

I have some prices / costs.

• I have an unknown value like 520.
• I have a top value that can be 520 or higher.
• I have a bottom value that can be 520 or lower.

Let's say the top value us 750 and I want to know how much more in percentage it is in compare to the 520 value.

((750/520)-1)*100 = 44%

• Does this value mean that 520 is 44% cheaper than 750?
• Does that value also mean that 750 is 44% more expensive than 520?

What I can recall is that we don't get the same percentage value up and down?

The number $750$ is $44\%$ more expensive than $520$, because $230 = 750 - 520$ is equal to $44\%$ of the value of $520$.

However, $520$ is NOT $44\%$ cheaper than $750$, because $230$ is not equal to $44\%$ of $750$. In fact, $230$ is only $31\%$ of $750$, so $520$ is $31\%$ cheaper than $750$.

If that's confusing you, then think about it this way:

If I have two potatoes, I have $100\%$ more potatoes than I would have if I only had one potato. But If I have one potato, I only have $50\%$ of the potatoes I would have if I had two, so I have $50\%$ less, not $100\%$ less.

• Ok, I got it. What if I would not use cheaper or more expensive, instead just say "The difference between the prices are this percentage"? Feb 6, 2015 at 8:36
• @JensTörnell You still have to specify the percentage of what. So, the difference between $750$ and $520$ is $44\%$ of $520$, and it is $31\%$ of $750$.
– 5xum
Feb 6, 2015 at 8:37