Quandaries
and Queries 

i'm a parent trying to calculate a percentage. if our cost is 54.00 and their cost is 117.00 what is the percentage of mark up? thanks 

Hi , If you are a merchant and you bought an item for $54.00 and then sold it to a customer for $117.00 then you marked it up $63.00 (63 = 117  54). But you want to express this as a percentage. When reporting a percentage you should always say percentage of what. From your perspective as the merchant you want to know "What is $63.00 as a percentage of what it cost me?" I think of this question as
and then I can translate it into an equation. "Percentage" means per 100, that is over 100, "what" is the quantity I don't know so I will call it x, "of" is multiplication and "is" is the equal sign. Thus the question is
Solving for x I get
Hence $63.00 is 116.7% of $54.00. Thus the markup is 116.7% in the sense that the markup is 116.7% of what it cost the merchant. From your customer's perspective the question might still be "What is $63.00 as a percentage of what it cost me?" but this time it means
which becomes
Solving for x this time gives
Hence $63.00 is 53.8% of $117.00. Thus the markup is 53.8% in the sense that the markup is 53.8% of what it cost your customer. So what is the percentage markup? This is a very ill formed question. If someone says to you that the markup is some percentage you need to ask "Percentage of what?" If you are reporting your markup you need to say "The markup is such and such percentage of my cost", and as a customer I need to say "The markup is such and such percentage of what it cost me". I hope this helps, 

