The Mathematics of Money

Copyright © 2008, The McGraw-Hill Companies, Inc.

In this chapter, we will follow a convention that the price a business pays for an item is

called the wholesale price or cost. The price a business sells the item for will be called the

retail price. We will use these terms even if the business purchases the item from a seller

that might not formally call itself a “wholesaler;” likewise, we will use these terms even if

the individual or business that sells the item is not strictly speaking a “retailer.”

Markup Based on Cost

One common method used for setting the selling price for an item is markup based on cost.

This method is straightforward and agrees with the way most people usually think about

setting prices. To determine a price with this method, we simply take the cost of the item,

and add on a predetermined percent of the item’s cost. For example, suppose that Eddie’s

Bike World can buy a particular model of bicycle for $255.00, and uses a mark up of 50%

based on cost. Fifty percent of $255 is (0.50)($255) 
 $127.50, and so adding this on

would mean a selling price of $225  $127.50 
 $352.50.

Finding the selling price in this way doesn’t require too much effort, but we can make

things even a bit simpler. A 50% markup means that every $1.00 of the cost turns into $1.00 

$0.50 
 $1.50 of selling price. So a $255 cost turns into 225($1.50) 
 $352.50 in selling

price. Using this logic allows us to fi nd the selling price with a bit less effort, and will also

pay off more richly in some of the problems that follow. We can sum this up in a formula:

FORMULA 8.1.1

Markup Based on Cost

P 
 C(1  r)

where

P represents the SELLING PRICE,

C represents the COST

and

r represents the PERCENT MARKUP

Example 8.1.1 An auto mechanic charges a 40% markup based on cost for parts.

What would the price be for an air fi lter that cost him $14.95? What is the dollar

amount of his markup on this item?

Since the markup is 40%, we multiply the cost by 1.40:

P 
 C( 1  r)

P 
 $14.95(1.40)

P 
 $20.93

The dollar amount of the markup can be determined in either of two ways. We can multiply

40% by the cost, to get (0.40)($14.95) 
 $5.98. Or we could subtract the cost from the

selling price to get $20.93  $14.95 
 $5.98. Whichever way we fi nd more convenient, the

result is the same.

We can also work backward to find cost if we know the selling price and the markup per-

cent. The following example will illustrate this.

Example 8.1.2 Hegel’s Bagels and Vienna Coffeehouse sells souvenir coffee mugs

for $7.95. The markup based on cost is 65%. Find (a) the cost of each mug, and

(b) the dollar amount of the markup.

(a) Working from our formula, we get:

P 
 C(1  r)

$7.95 
 C(1.65)

C 
 $4.82

(b) To fi nd the dollar amount of the markup we can subtract $7.95  $4.82 to get $3.13.

We could also have got this by multiplying (0.65)($4.82) 
 $3.13.

8.1 Markup and Markdown 333