Math CentralQuandaries & Queries


Question from Tammy:

How can a markup of 30% be calculated by using 1.43 times the original cost? Where does the 1.43 come from? For example: the original cost is 830.00 the markup is 30 %. The selling cost is 1186.90. My boss uses 1.43 to figure the mark up for 30% and 1.23 for 25% and 1.1 for 10%. What I want to know is how do they come up with these figures?

Hi Tammy.

Here's where your boss is getting this value: She is saying that 30% of the selling price is her markup. That means, for example, that 30% of $1186.90 is the markup (0.30 x $1186.90 = $356.07). If you add that to the original cost of $830, you get $1186.07, which is very close to the selling price (the difference is due to rounding).

So it is a matter of perspective. 30% of the final price is the amount you add to the original cost.

Now take a look from this perspective: If 30% of the final cost is the markup, then the original cost is 70% of the final price, right?

But when you have the original cost and need to know the final price, then you have a figure that is 70% of the final price, but you want the 100% price. So you multiply by 100%/70% which is 10/7 which is 1.43 !

Mathematically, we say that if C is the original cost and P is the final price, then

70% x P = 100% x C

If you have the final price P and want the original cost C, then you solve this for C:

C = P x 70% / 100% = P x 0.7

But if you have the original cost C and want to know what final price you should sell for in order to get the 30% markup, then you solve for P instead:

P = C x 100% / 70% = C x 1.43

There is some debate over whether or not this should be called "markup" or "margin" or something else. Do a search on the word "markup" in your dictionary or on our site to find out more about the words and how they are used in different situations.

Stephen La Rocque


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