The Mathematics of Money

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

8.1 Markup and Markdown 335

We can make things even a bit simpler, just as we did with markup based on cost.

A 10% markdown means that every $1.00 of the cost turns into $1.00  $0.10 
 $0.90

of selling price. So a $352.50 price turns into $352.50(0.90) 
 $317.25. Just as with

markup, using this logic allows us to fi nd the marked down 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 8.1.2

Markdown

MP 
 OP(1  d)

where

MP represents the MARKED-DOWN PRICE,

OP represents the ORIGINAL PRICE

and

d represents the PERCENT MARKDOWN

Note that this formula for discount very closely parallels the formula for markup. Note

also, though, that while the markup percent is a percent of the cost, the markdown percent

is a percent of the marked-up retail price.

Example 8.1.4 At its Presidents’ Day Sale, a furniture store is offering 15% off

everything in the store. What would the sale price be for a sofa that normally sells for

$1,279.95? What is the dollar amount of the markdown?

Since the markdown is 15%, we multiply the original price by 0.85:

MP 
 OP(1  d)

MP 
 $1,279.95(0.85)

MP 
 $1,087.96

The dollar amount of the markdown can be determined in either of two ways. We can multi-

ply 15% by the original price to get (0.15)($1,279.95) 
 $191.99. Or we could subtract the

cost from the selling price to get $1,279.95  $1,087.96 
 $191.99. Whichever way we

fi nd more convenient, the result is the same.

Again, as we did with markup, we can turn things around and fi nd the original price based

on the marked down price and markdown percent.

Example 8.1.5 Hal’s Hardware Haven is having a going–out-of-business sale.

According to its ad, everything in the store is marked down 40%. If a set of patio lights

is offered at a marked-down price of $29.97, what was the original price? How much

of a dollar savings is this versus the original price?

Working from our formula, we get:

MP 
 OP(1  d)

$29.97 
 OP(0.60)

OP 
 $49.95

To fi nd the dollar amount of the markdown we can subtract $49.95  $29.97 to get $19.98.

We could also have gotten this by multiplying (0.40)($49.95) 
 $19.98.

The same cautions are in order with markdown as with markup. We have to be very careful

to make sure we are clear just what the percent is of. In the case of markdown, the percent

is a percent of the original price. It is not a percent of the marked down price. It would be

incorrect to apply the 40% markdown rate to the marked-down price to fi nd the amount of

the markdown.

Once again, parallel to what we did with markup, we can fi nd the percent markdown if

we know the original and marked down price.