Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges
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Although many businesses base their markup on cost, many others, often retailers,
commonly use a percent of selling price—that is, they use markup based on selling
price. That doesn’t mean that selling price is determined without considering cost or
even before considering cost. It merely means that the dollar markup is computed by
multiplying the markup percent by the selling price.
Many individuals start their own business when they observe another successful
business selling a product. New owners believe that they can acquire the product, pay all
expenses, and still sell it for less than the existing business is selling its product. Instead
of basing the selling price on costs, expenses, and satisfactory profit, the new owners may
price their product just under the competition’s price. They base their selling price on
the competition’s selling price rather than marking up from their own costs.
Basing markup calculations on selling price can be an advantage in a retail store where
the salesperson or sales manager has the authority to lower the sales price immediately in
order to make a sale. In a larger business, these persons may not even know the exact cost.
144 Part 2 Percentage Applications
Computing Markup Based on Selling Price
4
Learning Objective
Compute the markup variables when
the markup percent is based on
selling price.
8.4 Emphasize that the same markup
percent will result in different amounts
of dollar markup,depending on whether
markup is based on cost (C) or selling
price (SP).
Likewise,the same dollar markup
will result in different markup per-
cents.Here are the formulas to convert
the markup percents from one base to
the other:
Markup % (on SP) 5 Markup %
(on C) 4 [100% 1 Markup %
(on C)]
Markup % (on C) 5 Markup %
(on SP) 4 [100% 2 Markup %
(on SP)]
Possible discussion questions:
Can markup percent based on cost
equal 100%? Yes
Can markup percent based on cost
exceed 100%? Yes
Can markup percent based on sell-
ing price equal 100%? Not really,be-
cause then the cost would be zero and
the markup percent based on cost
would be infinite.
Can markup percent based on
selling price exceed 100%? Not really,
because then the cost would be neg-
ative (maybe the “seller”was paid by
someone to take the item away).
to Compute the Cost Based on Selling Price
1. Multiply the selling price by the markup percent to get the dollar markup.
2. Subtract the dollar markup from the selling price to get the cost.
STEPS
EXAMPLE F
Roy Brainard enters Floyd’s Appliance Store to buy a washing machine. He finds one
with a selling price of $400. He knows that he can buy it for $375 at another store, but he
prefers this store because of its reputation for good service. He tells the sales manager,
“I would buy it for $375.” The manager, Jesse Cullen, knows that the markup percent is
40% based on selling price. What was Jesse’s cost for the washing machine?
Dollar markup 5 Markup percent 3 Selling price 5 0.40 3 $400 5 $160
Cost 5 Selling price 2 Dollar markup 5 $400 2 $160 5 $240
Jesse can then decide whether she prefers a sale for which she gets a $135 markup or no sale
for which she hopes to have a $160 markup. Although it would be helpful if Jesse knew how
much markup she would need to pay for expenses, at least she would know the cost.
STEP 2
STEP 1
EXAMPLE G
Find the dollar markup and the cost of an item that sells for $120 and has a markup
percent that is 30% based on selling price.
Dollar markup 5 Markup percent 3 Selling price 5 0.30 3 $120 5 $36
Cost 5 Selling price 2 Dollar markup 5 $120 2 $36 5 $84
STEP 2
STEP 1
COMPUTING COST DIRECTLY FROM SELLING PRICE
When you know the selling price and the markup percent (based on selling price), you
can compute the cost directly, wihout computing the dollar markup.
COMPUTING SELLING PRICE DIRECTLY FROM COST
Likewise, you can use the reverse procedure to compute the selling price directly from the
cost and the markup percent (based on selling price), without computing the dollar markup.
Chapter 8 Markup 145
Markup Based on
Cost/Selling Price
Video
to Compute the Cost Directly from the Selling Price
1. Subtract the markup percent from 100%.
2. Multiply this difference by the selling price to get the cost.
STEPS
EXAMPLE H
What is the cost of an item that has a selling price of $240 and a markup percent of 60%
based on selling price?
100% 2 Markup percent 5 100% 2 60% 5 40%
Cost 5 (100% 2 Markup percent) 3 Selling price 5 0.40 3 $240 5 $96
STEP 2
STEP 1
to Compute the Selling Price Directly from the Cost
1. Subtract the markup percent from 100%.
2. Divide the cost by this difference to get the selling price.
STEPS
EXAMPLE I
The cost of a mountain bike is $120. The markup percent based on
selling price is 40%. Find the selling price.
100% 2 Markup percent 5 100% 2 40% 5 60%
Selling price 5 Cost 4 (100% 2 Markup percent) 5
$120 4 0.60 5 $200
You can always check your work in markup problems:
Selling price is $200, and markup percent is 40% based on selling price.
Dollar markup 5 Markup percent 3 Selling price 5 0.40 3 $200 5 $80
Cost 5 Selling price 2 Dollar markup 5 $200 2 $80 5 $120
It checks!
STEP 2
STEP 1
Compute the required values when the markup percent is based on selling price.
a. Selling price 5 $750; Markup percent 5 50% Dollar markup 5 0.50 3 $750 5 $375
Find dollar markup, and then find cost. Cost 5 $750 2 $375 5 $375
b. Selling price 5 $40; Markup percent 5 30% 100% 2 Markup percent 5 100% 2 30% 5 70%
Find 100% 2 Markup percent, and then find cost directly. Cost 5 0.70 3 $40 5 $28
c. Cost 5 $150; Markup percent 5 40% 100% 2 Markup percent 5 100% 2 40% 5 60%
Find 100% 2 Markup percent, and then find selling price directly. Selling price 5 $150 4 0.60 5 $250
✔
CONCEPT CHECK 8.4
© DAVID CHADWICK/ISTOCKPHOTO INTERNATIONAL
In the illustration for Athletes’ World, the pair of athletic shoes had a cost of $43.50. The
store owner decided that the selling price of the athletic shoes would be $79.95. The
markup percent based on selling price can be calculated in two steps.
146 Part 2 Percentage Applications
Computing Markup Percent Based
on Selling Price
5
Learning Objective
Compute markup percent based on
selling price.
to Compute the Markup Percent from the Selling Price
1. Subtract the cost from the selling price to get the dollar markup.
2. Divide the dollar markup by the selling price to get the markup percent.
STEPS
For Athletes’ World’s athletic shoes,
Dollar markup 5 Selling price 2 Cost 5 $79.95 2 $43.50 5 $36.45
Markup percent 5 Dollar markup 4 Selling price 5 $36.45 4 $79.95 5
0.456, or 45.6% (rounded to one decimal place)
STEP 2
STEP 1
EXAMPLE J
What is the markup percent based on selling price when the selling price is $80 and the
cost is $50?
Dollar markup 5 Selling price 2 Cost 5 $80 2 $50 5 $30
Markup percent 5 Dollar markup 4 Selling price 5 $30 4 $80 5 0.375,
or 37.5%
STEP 2
STEP 1
EXAMPLE K
What is the markup percent based on selling price when the dollar markup is already
known to be $150 and the selling price is $375? (Step 1 is not necessary.)
Markup percent 5 Dollar markup 4 Selling price 5 $150 4 $375 5 0.40,
or 40%
STEP 2
Cost 5 $1,600; Selling price 5 $2,560 Dollar markup 5 $2,560 2 $1,600 5 $960
Find the markup percent based on selling price. Markup percent 5 $960 4 $2,560 5 0.375, or 37.5%
COMPLETE ASSIGNMENT 8.2.
✔
CONCEPT CHECK 8.5
Chapter 8 Markup 147
cost of goods sold markup percent
dollar markup markup percent based on cost
markup markup rate
markup based on selling price
Chapter Terms for Review
Try Microsoft
®
Excel
Try working the problems using the Microsoft Excel templates found on your student
CD. Solutions for the problems are also shown on the CD.
148 Part 2 Percentage Applications
THE BOTTOM LINE
Summary of chapter learning objectives:
Learning Objective
8.1
Compute the variables in the basic markup formula.
Example
Find the missing variables in the basic markup formula:
1. Cost 5 $231.50; Dollar markup 5 $109.12
2. Cost 5 $34.20; Selling price 5 $59.95
3. Dollar markup 5 $475; Selling price 5 $900
Answers: 1. Selling price 5 $340.62 2. Dollar markup 5 $25.75 3. Cost 5 $425 4. a. $280; $1,080 b.135%; $1,080
5. 140%; $1,500 6. 35% 7. a. $205; $615 b. 75%; $615 8. 60%; $2,250 9. 25%
8.2
Compute the markup variables when the markup per-
cent is based on cost.
8.3
Compute the markup percent based on cost.
8.4
Compute the markup variables when the markup per-
cent is based on selling price.
8.5
Compute the markup percent based on selling price.
4. Cost 5 $800; Markup percent 5 35%
a. Find the dollar markup and then find the selling price.
b. Find 100% 1 Markup percent, and then find the selling price.
5. Selling price 5 $2,100; Markup percent 5 40%
Find 100% 1 Markup percent, and then find the cost.
6. Cost 5 $80; Selling price 5 $108
Find the markup percent based on cost.
7. Selling price 5 $820; Markup percent 5 25%
a. Find the dollar markup and then find the cost.
b. Find 100% 2 Markup percent and then find the cost.
8. Cost 5 $1,350; Markup percent 5 40%
Find 100% 2 Markup percent, and then find the selling price.
9. Cost 5 $825; Selling price 5 $1,100
Find the markup percent based on the selling price.
Chapter 8 Markup 149
SELF-CHECK
Review Problems for Chapter 8
1 Find the missing terms.
Cost of Dollar Selling Cost of Dollar Selling
Goods Sold Markup Price Goods Sold Markup Price
a. $28.90 $14.45 c. $1,405 $2,975
b. $188.12 $399.95 d. $426.25 $998.88
In problems 2–9, the markup percent is based on cost. Find the missing terms. Round all percents to the
nearest one tenth of a percent.
100% 1
Markup Dollar Selling Markup Markup Selling
Cost Percent Markup Price Cost Percent Percent Price
2 $500 50% a. b. 4 $225 60% a. b.
3 $36 65% a. b. 5 $240 75% a. b.
100% 1
Selling Markup Markup Selling Dollar Markup
Price Percent Percent Cost Price Cost Markup Percent
6 $1,012 100% a. b. 8 $540 $240 a. b.
7 $98 40% a. b. 9 $2,000 $1,600 a. b.
In problems 10–17 the markup percent is based on selling price. Find the missing terms. Round all
percents to the nearest one tenth of a percent.
100% 2
Selling Markup Dollar Selling Markup Markup
Price Percent Markup Cost Price Percent Percent Cost
10 $240 30% a. b. 12 $1,240 40% a. b.
11 $144 25% a. b. 13 $528 75% a. b.
100% 2
Markup Markup Selling Selling Dollar Markup
Cost Percent Percent Price Price Cost Markup Percent
14 $960 60% a. b. 16 $800 $480 a. b.
15 $36 25% a. b. 17 $3,750 $1,500 a. b.
18 Carol Wilson sells high-end toys, specializing in all wooden toys for preschool children. She pays $40 for a toy
truck. Carol sells the toy truck for $50. a. Find the dollar markup. b. Find the markup percent based on
cost. c. Find the markup percent based on selling price.
Answers to the Self-Check can be found in Appendix B at the back of the text.
150 Part 2 Percentage Applications
Notes
Chapter 8 Markup 151
Assignment 8.1: Markup Based on Cost
Name
Date Score
A (12 points) Calculate the missing terms. (2 points for each correct answer)
Dollar Selling Dollar Selling
Cost Markup Price Cost Markup Price
1. $480.70 $175.25 2. $48.51 $69.95
$21.44$655.95
Learning Objectives
1 2 3
$480.70 1 $175.25 5 $655.95 $69.95 2 $48.51 5 $21.44
3. $374.50 $829.98 4. $175.50 $57.50
$233.00$455.48
$829.98 2 $374.50 5 $455.48 $175.50 1 $57.50 5 $233.00
5. $629.00 $909.99 6. $352.49 $749.49
$397.00$280.99
$909.99 2 $629.00 5 $280.99 $749.49 2 $352.49 5 $397.00
Score for A (12)
B (32 points) In the following problems, the markup percent is based on cost. Find the missing terms.
(2 points for each correct answer)
100% 1
Markup Dollar Selling Markup Markup Selling
Cost Percent Markup Price Cost Percent Percent Price
7. $850 40% 8. $160 125%
$360225%$1,190$340
0.40 3 $850 5 $340 100% 1 125% 5 225%
$850 1 $340 5 $1,190 2.25 3 $160 5 $360
9. $1,500 70% 10. $240 100%
$480.00200%$2,550$1,050
0.70 3 $1,500 5 $1,050 100% 1 100% 5 200%
$1,500 1 $1,050 5 $2,550 2.0 3 $240 5 $480
11. $640 75% 12. $800 30%
$1,040130%$1,120$480
0.75 3 $640 5 $480 $100 1 30% 5 130%
$640 1 $480 5 $1,120 1.3 3 $800 5 $1,040
13. $2,500 90% 14. $150 210%
$465310%$4,750$2,250
0.9 3 $2,500 5 $2,250 100% 1 210% 5 310%
$2,500 1 $2,250 5 $4,750 3.1 3 $150 5 $465
Score for B (32)
C (32 points) In the following problems, the markup percent is based on cost. Find the missing terms.
Round all percents to the nearest tenth of a percent. (2 points for each correct answer)
100% 1
Selling Markup Markup Selling Dollar Markup
Price Percent Percent CostPrice Cost Markup Percent
15. $1,240 60% 16. $48 $30
60%$18$775160%
152 Part 2 Percentage Applications
Assignment 8.1 Continued
100% 1 60% 5 160%; $1,240 4 1.60 5 $775 $48 2 $30 5 $18; $18 4 $30 5 0.6
17. $110 120% 18. $1,922 $1,240
55%$682$50220%
100% 1 120% 5 220%; $110 4 2.2 5 $50 $1,922 2 $1,240 5 $682; $682 4 $1,240 5 0.55
19. $594 35% 20. $679 $388
75.0%$291$440135%
100% 1 35% 5 135%; $594 4 1.35 5 $440 $679 2 $388 5 $291; $291 4 $388 5 0.75
21. $2,250 50% 22. $216 $96
125%$120$1,500150%
100% 1 50% 5 150%; $2,250 4 1.5 5 $1,500 $216 2 $96 5 $120; $120 4 $96 5 1.25
Score for C (32)
D (24 points) Business Applications. In the following problems, the markup percent is based on cost.
Round all percents to the nearest tenth of a percent. (3 points for each correct answer)
23. Susan Chin owns a firm that sells office furniture to local businesses. One set of six matched pieces costs
Susan $2,100. To cover her own business expenses and allow a reasonable profit, Susan marks up this set
by 75% of the cost. Find the dollar markup and the selling price.
Dollar markup
Selling price
24. Stan Wegner manufactures a handheld heart monitoring device. He sells it for $840, which represents a
markup of 275% on his production cost. Stan marks it up this much to cover additional business ex-
penses and profit as well as product development. Find Stan’s production cost and the dollar markup.
Cost
Dollar markup
25. Sentry Security Systems sells burglar and fire alarm systems for homes and small businesses. One basic
system costs Sentry $720. Sentry marks up the alarm system by $396. Find the selling price, and find the
markup percent based on cost.
Selling price
Markup percent
26. After Matt Lord drove his father’s car with no oil, the car needed a new engine. A local mechanic charged
Matt’s father $2,250 for a rebuilt engine that cost the mechanic $1,800. All labor was additional. Compute
the dollar markup and the markup percent based on the cost of the engine.
Dollar markup
Markup percent
Score for D (24)
$450 4 $1,800 5 0.25, or 25%
25%
$2,250 2 $1,800 5 $450
$450
$396 4 $720 5 0.55, or 55%
55%
$720 1 $396 5 $1,116
$1,116
$840 4 3.75 5 $224
$616
$840 2 $224 5 $616100% 1 275% 5 375%
$224
$2,100 1 $1,575 5 $3,675
$3,675
0.75 3 $2,100 5 $1,575
$1,575
Chapter 8 Markup 153
Assignment 8.2: Markup Based on Selling Price
Name
Date Score
A (12 points) Calculate the missing terms. (2 points for each correct answer)
Dollar Selling Dollar Selling
Cost Markup Price Cost Markup Price
1. $67.34 $82.15 2. $193.19 $458.88
$265.69$149.49
Learning Objectives
1 4 5
$67.34 1 $82.15 5 $149.49 $458.88 2 $193.19 5 $265.69
3. $840 $2,659 4. $789.25 $476.50
$1,265.75$1,819
$2,659 2 $840 5 $1,819 $789.25 1 $476.50 5 $1,265.75
$99.99 2 $62.50 5 $37.49 $978.95 2 $307.15 5 $671.80
Score for A (12)
B (32 points) In the following problems, the markup percent is based on selling price. Find the missing
terms. (2 points for each correct answer)
100% 2
Selling Markup Dollar Selling Markup Markup
Price Percent Markup CostPrice Percent Percent Cost
7. $120 55% 8. $150 25%
$112.5075%$54$66
0.55 3 $120 5 $66 100% 2 25% 5 75%
$120 2 $66 5 $54 0.75 3 $150 5 $112.50
9. $360 40% 10. $1,260 35%
$81965%$216$144
0.40 3 $360 5 $144 100% 2 35% 5 65%
$360 2 $144 5 $216 0.65 3 $1,260 5 $819
11. $1,998 50% 12. $75 70%
$22.5030%$999$999
0.50 3 $1,998 5 $999 100% 2 70% 5 30%
$1,998 2 $999 5 $999 0.30 3 $75 5 $22.50
13. $824 60% 14. $640 65%
$22435%$329.60$494.40
0.60 3 $824 5 $494.40 100% 2 65% 5 35%
$824 2 $494.40 5 $329.60 0.35 3 $640 5 $224
Score for B (32)
5. $62.50 $99.99 6. $307.15 $978.95
$671.80$37.49