Markups and Discounts

Date: 02/12/2002 at 09:43:46
From: Gary Budzak
Subject: Markup and discount

Dear Dr. Math,

I have been selling products over the past 30 years, and I still run 
into this question.

What is the correct way to markup or discount a product?

$100 markup (x) 1.1 = $110 = 10%
$100 markup (/) .9  = $111.11 = 10%

$100 discount (/) 1.1 = $90.90 = 10%
$100 discount  (.9)   = $90    = 10%

I find it easier to mark up (/) .9 .8, which equal 10% 20% etc., and 
then mark down (x) .9, .8, .7, which equal 10 to 30%. It seems faster 
if there is no other explanation.  

I have yet to find anyone who can explain it to me.
Thanks,
Gary B.

Date: 02/12/2002 at 12:35:18
From: Doctor Peterson
Subject: Re: Markup and discount

Hi, Gary.

If you mark up by 10%, you are adding 0.10 to the price of an item:

    new price = old price + 0.10 * old price
              = 1 * old price + 0.10 * old price
              = old price * (1.10)

(I am using "*" for multiplication.)

To determine the original price given the marked up price, you have to 
undo this by dividing:

    old price = new price / 1.10

If you discount by 10%, you are subtracting 0.10 of the price of the 
item:

    new price = old price - 0.10 * old price
              = old price * (0.90)

To determine the original price given the discounted price, you have 
to undo this by dividing:

    old price = new price / 0.90

Note that if you mark up by 10% and then discount by 10%, you don't 
get back the original value, because you are taking off 10% of a 
larger amount:

    $100 * 1.10 * 0.9 = $110 * 0.9 = $99

Here we took off $11 for the discount, not the $10 we added in the 
markup.

I think this differs from what you wrote, if I understand it 
correctly. You always use 1.10 (1 plus the percentage) for markups, 
and 0.90 (1 minus the percentage) for discounts. You multiply to apply 
the markup or discount, and divide to undo it.

Here are some relevant discussions in our archive:

   Restoring an Original Price
   http://mathforum.org/dr.math/problems/mojoe54.8.6.96.html   

   Price before Discount
   http://mathforum.org/dr.math/problems/dickenson.6.3.96.html   

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/