Larry,
Percentage is a word we all use and sometimes quite sloppily. Every time you use the word percent or read it or hear it you should think "Percent OF WHAT?"
If you buy an item for $100 and mark it up to $115 and sell it to a customer, then the markup is $15. This $15 is 15% OF WHAT IT COST YOU. (15% of $100 is $15)
If you buy an item for $100 and mark it up to $117.65 and sell it to a customer, then the markup is $17.65. This $17.65 is 15% OF WHAT IT COST YOUR CUSTOMER. (15% of $117.65 is $17.65)
This second interpretation can be said another way. Suppose that you are going to charge your customer $x and you want the markup to be 15% of $x, then your cost ($100) is 85% of $x. That is
0.85 $x = $100 so $x = ^{$100}/_{0.85} = $117.65
If I were your customer I would argue vehemently that $117.65 is a 17.65% markup! If you are in a restaurant, the bill is $100 and you want to leave a 15% tip do you leave a tip of $15 or $17.65?
Penny
