Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges
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134 Part 2 Percentage Applications
Notes
Chapter 7 Discounts 135
Assignment 7.1: Trade Discounts
Name
Date Score
A (24 points) Problems 1–3: Find the dollar amount of the trade discount and the net price, using the
discount method. Problems 4–6: Find the complement rate and the net price, using the complement
method. (2 points for each correct answer)
Trade ListDiscount Net
Discount Price Amount Price
1. 35% $1,260
2. 30% $6,470
3. 25% $8,480
Trade List Complement Net
Discount Price Rate Price
4. 30% $1,670
5. 20% $6,990
6. 35% $4,720
Score for A (24)
B (16 points) Find the amount of each discount in the given series of trade discounts.Then find the net
price.Where a discount amount doesn’t exist write a dash. (2 points for each correct answer)
ListTrade
Trade Discount Amounts
Net
Price Discounts First Second Third Price
7. $2,400 30%, 25%
$1,260—$420$720
$3,06865%
$5,59280%
$1,16970%
$6,360$2,120
$4,529$1,941
$819$441
0.35 3 $1,260 5 $441
$1,260 2 $441 5 $819
0.30 3 $6,470 5 $1,941
$6,470 2 $1,941 5 $4,529
0.25 3 $8,480 5 $2,120
$8,480 2 $2,120 5 $6,360
100% 2 30% 5 70%
0.70 3 $1,670 5 $1,169
100% 2 20% 5 80%
0.80 3 $6,990 5 $5,592
100% 2 35% 5 65%
0.65 3 $4,720 5 $3,068
0.30 3 $2,400 5 $720 0.25 3 $1,680 5 $420
$2,400 2 $720 5 $1,680 $1,680 2 $420 5 $1,260
8. $1,600 40%, 25%, 20%
$576$144$240$640
0.40 3 $1,600 5 $640 0.25 3 $960 5 $240 0.20 3 $720 5 $144
$1,600 2 $640 5 $960 $960 2 $240 5 $720 $720 2 $144 5 $576
Score for B (16)
1
Learning Objectives
2 3
C (20 points) Find the complement rate for each discount in the given series of trade discounts.Then
find the net price, using the complement method.Where a complement rate doesn’t exist write a dash.
(2.5 points for each correct answer)
ListTrade
Complement Rates
Net
Price Discounts First Second Third Price
9. $1,800 40%, 20%
$864—80%60%
136 Part 2 Percentage Applications
Assignment 7.1 Continued
100% 2 40% 5 60%
100% 2 20% 5 80%
0.60 3 0.80 3 $1,800 5 $864
10. $2,000 40%, 20%, 10%
$86490%80%60%
100% 2 40% 5 60%
100% 2 20% 5 80%
100% 2 10% 5 90%
0.60 3 0.80 3 0.90 3 $2,000 5 $864
Score for C (20)
D (20 points) Find the complement rate for each discount in the given series of trade discounts.Then find
the equivalent single discount rate, to the nearest of a percent. (2.5 points for each correct answer)
Trade
Complement Rates
Equivalent Single
Discounts First Second Third Discount Rates
11. 30%, 20%, 5%
46.8%95%80%70%
1
10
100% 2 30% 5 70% 100% 2 20% 5 80% 100% 2 5% 5 95%
0.70 3 0.80 3 0.95 5 0.532 1.000 2 0.532 5 0.468, or 46.8%
12. 20%, 10%, 5%
31.6%95%90%80%
100% 2 20% 5 80% 100% 2 10% 5 90% 100% 2 5% 5 95%
0.80 3 0.90 3 0.95 5 0.684 1.000 2 0.684 5 0.316, or 31.6%
Score for D (20)
E (20 points) Solve each of the following business applications about trade discounts. Use either the
discount method or the complement method. (10 points for each correct answer)
13. Gifford Landscaping, Inc., purchased $425 worth of plants and $180 worth of soil and fertilizer from a
garden supply wholesaler. The wholesaler gives Gifford a 20% trade discount on the plants and a 30% trade
discount on the other items. Compute the net price that Gifford Landscaping will be required to pay.
$466
0.20 3 $425 5 $85 $425 2 $85 5 $340 plants
0.30 3 $180 5 $54 $180 2 $54 51
126 soil, etc.
$466 total
14. Hackett Roofing is purchasing redwood shakes to reroof a house. The shakes have a list price of $15,600.
The Pacific Roofing Supply Company gives Hackett the normal trade discount of 25%. In addition,
Pacific gives Hackett two further trade discounts of 20% and 10% because of the large volume of busi-
ness that the company has done with Pacific so far this year. What is Hackett’s net price on the order of
redwood shakes?
$8,424
100% 2 25% 5 75%
100% 2 20% 5 80%
100% 2 10% 5 90%
0.75 3 0.80 3 0.90 3 $15,600 5 $8,424
Score for E (20)
Chapter 7 Discounts 137
Assignment 7.2: Cash Discounts
Name
Date Score
A (64 points) For the following problems, find the discount date, the due date, the amount of the cash
discount, and the amount of the remittance. (2 points for each correct date and 6 points for each correct
amount)
1.
Terms: 3/5, n/25 Discount date:
Invoice date: May 27 Due date:
Invoice amount: $2,875.12 Discount amount:
Remittance:
$2,788.87
$86.25
June 21
June 1
Learning Objectives
4 5
Disc. date: May 27 1 5 5 June 1
Due date: May 27 1 25 5 June 21
0.03 3 $2,875.12 5 $86.2536, or $86.25
$2,875.12 2 $86.25 5 $2,788.87
2. Terms: 2/10, n/30 Discount date:
Invoice date: July 23 Due date:
Invoice amount: $484.86 Discount amount:
Freight: $45.00 Remittance:
$476.06
$8.80
Aug. 22
Aug. 2
Disc. date: July 23 1 10 5 Aug. 2
Due date: July 23 1 30 5 Aug. 22
$484.86 2 $45 5 $439.86
0.02 3 $439.86 5 $8.7972, or $8.80
$439.86 2 $8.80 1 $45 5 $476.06
3. Terms: 1.5/15, net 45 Discount date:
Invoice date: Aug. 20 Due date:
Invoice amount: $692.00 Discount amount:
Returned goods: $242.00 Remittance:
$443.25
$6.75
Oct. 4
Sept. 4
Disc. date: Aug. 20 1 15 5 Sept. 4
Due date: Aug. 20 1 45 5 Oct. 4
$692 2 $242 5 $450
0.015 3 $450 5 $6.75
$450 2 $6.75 5 $443.25
4. Terms: 1.5/20, n/60 Discount date:
Invoice date: July 26 Due date:
Invoice amount: $1,645.55 Discount amount:
Returned goods: $498.75 Remittance:
Freight: $80.00
$1,130.80
$16.00
Sept. 24
Aug. 15
Disc. date: July 26 1 20 5 Aug. 15
Due date: July 26 1 60 5 Sept. 24
$1,645.55 2 $498.75 2 $80 5 $1,066.80
0.015 3 $1,066.80 5 $16.00
$1,066.80 2 $16.00 1 $80 5 $1,130.80
Score for A (64)
B (16 points) For the following problems, find the discount date, the complement rate, and the amount of
the remittance. (2 points for each date and rate; 4 points for each correct remittance)
5. Terms: 2/10, n/35 Discount date:
Invoice date: March 29 Complement rate:
Invoice amount: $582.50 Remittance:
$570.85
98%
Apr. 8
138 Part 2 Percentage Applications
Assignment 7.2 Continued
Disc. date: Mar. 29 1 10 5 Apr. 8
Comp rate: 100% 2 2% 5 98%
0.98 3 $582.50 5 $570.85
6. Terms: 1/25, net 75 Discount date:
Invoice date: July 9 Complement rate:
Invoice amount: $2,684.92 Remittance:
Returned goods: $171.12
Freight: $45.00
$2,489.11
99%
Aug. 3
Disc. date: July 9 1 25 5 Aug. 3 $2,444.11 1 $45 5 $2,489.11
Comp. rate: 100% 2 1% 5 99%
$2,684.92 2 $171.12 2 $45.00 5 $2,468.80
0.99 3 $2,468.80 5 $2,444.112, or $2,444.11
Score for B (16)
C (20 points) The following problems involve partial payments made within the discount period. Solve for
the items indicated. (5 points for each correct answer)
7. Terms: 4/5, n/20 Amount credited:
Invoice date: Feb. 28 Remittance: $600
Invoice amount: $981.94 Unpaid balance:
$356.94
$625.00
Comp. rate: 100% 2 4% 5 96%
$600 4 0.96 5 $625.00
$981.94 2 $625.00 5 $356.94
8. Terms: 2/15, net 40 Amount credited:
Invoice date: Feb. 15 Remittance: $500
Invoice amount: $832.90 Unpaid balance:
Returned goods: $186.00
$136.70
$510.20
Comp. rate: 100% 2 2% 5 98%
$500 4 0.98 5 $510.2041, or $510.20
$832.90 2 $186 2 $510.20 5 $136.70
Score for C (20)
Markup
Chapter 8 Markup 139
Learning Objectives
By studying this chapter and completing all assignments, you will be able to:
Compute the variables in the basic markup formula.
Compute the markup variables when the markup percent is based
on cost.
Compute markup percent based on cost.
Compute the markup variables when the markup percent is based
on selling price.
Compute markup percent based on selling price.
8
1
Learning Objective
2
Learning Objective
3
Learning Objective
4
Learning Objective
5
Learning Objective
Some businesses manufacture products and sell them. Other businesses buy products from
someone else and then resell them. Both types of businesses must sell their products for
more than it costs to produce or purchase them. This price increase is called the markup.
Athletes’ World is a chain of retail stores that sells athletic equipment and athletic
clothing. The store buys shoes directly from a manufacturer. Suppose that the manufac-
turer charges $43.00 per pair for one particular type of athletic shoe. The prorated
amount to deliver one pair to the store is $0.50. The total cost of the shoes, with delivery,
is $43.50. $43.50 is called the cost of goods sold, or just the cost.
If Athletes’ World sells the shoes for exactly the cost, $43.50, it will actually lose
money on the sale. The store has many other expenses—such as rent, utilities, and
salaries—that are not part of the cost of acquiring the shoes. Athletes’ World must mark
up the selling price far enough above the cost of the shoes to cover all these additional
costs—and also leave some profit for the owners.
The total amount that Athletes’ World marks up the selling price is called the dollar
markup. (Note: Markup is expressed both in dollars and in percents. To eliminate
confusion, in this book we use two separate terms: dollar markup and markup percent.)
Suppose that the accountants for Athletes’ World estimate that $18.80 of additional
expenses should be allocated to each pair of athletic shoes. Also, suppose that the store
would like a profit of $16.00 on each pair of shoes. Then the total dollar markup that it
should give the shoes is $18.80 1 $16.00 5 $34.80.
To determine the selling price of the shoes, Athletes’ World adds the dollar markup to
the cost of goods sold (cost), using the basic markup formula:
140 Part 2 Percentage Applications
Computing Markup Variables
1
Learning Objective
Compute the variables in the basic
markup formula.
8.1 You may want to mention that
these numbers are used only for
purposes of illustration.The store buys
shoes in quantities,and the prices and
the freight are also for quantities.Also,
taxes are not included in this discus-
sion.Finally,not all shoes will sell at a
price that gives the desired profit.
Some sizes and styles left at the end of
the season may sell if the price is
marked low enough.
© MICHAEL CONROY/ASSOCIATED PRESS
Compute the missing terms in the three markup formulas:
a. Cost 5 $417.82; Dollar markup 5 $204.20 Selling price 5 Cost 1 Dollar markup
5 $417.82 1 $204.20 5 $622.02
b. Cost 5 $154.40; Selling price 5 $392.12 Dollar markup 5 Selling price 2 Cost
5 $392.12 2 $154.40 5 $237.72
c. Dollar markup 5 $41.26; Selling price 5 $93.20 Cost 5 Selling price 2 Dollar markup
5 $93.20 2 $41.26 5 $51.94
✔
CONCEPT CHECK 8.1
Selling price 5 Cost 1 Dollar markup 5 $43.50 1 $34.80 5 $78.30
Because the dollar markup is the difference between the selling price and
the cost of goods sold, it is sometimes useful to rewrite the formula as
Dollar markup 5 Selling price 2 Cost 5 $78.30 2 $43.50 5 $34.80
Likewise, cost is the difference between selling price and dollar markup. Thus,
Cost 5 Selling price 2 Dollar markup 5 $78.30 2 $34.80 5 $43.50
In the example, Athletes’ World computed its markup directly by determining its
expenses and the desired profit. However, this method isn’t practical when a business has
hundreds or thousands of items. Allocating expenses and profit to each item would be
too tedious. A more practical method is for the owner, an employee, or an accountant to
analyze prior sales of the company or a similar company. The analyst can look at the
costs of goods, additional expenses, and desired profit to determine a percent to use to
mark up various items, called the markup percent.
One company may use different markup percents for different types of items. For
example, an appliance store often performs repair services and sells replacement parts
for the appliances it sells. The store may have one markup percent for the actual appli-
ance, a second markup percent for repair services, and a third markup percent for re-
placement parts.
In Chapter 5 on percents, we introduced three terms: rate, base, and percentage. In
this chapter, rate is the markup percent, or markup rate. Percentage is the dollar markup.
Determining the base is more challenging because sometimes cost is the base and some-
times selling price is the base. For some businesses, cost may be the more logical base for
calculating dollar markup. However, calculating dollar markup based on selling price is
an advantageous method for many retail stores.
The accountant for Athletes’ World says that, in order to pay all expenses and have
a reasonable profit, and based upon a cost of $43.50, the company’s markup should be
80% of the cost. When the cost and the markup percent are known, the dollar markup
and the selling price can be computed.
Chapter 8 Markup 141
Computing Markup Based on Cost
Compute the markup variables when
the markup percent is based on cost.
2
Learning Objective
8.2 Most students will already be
aware that the percent of markup
varies with the type of business and
also the type of product.A high-
volume supermarket may have low
markups on many staples but higher
markups on snack foods and even
higher markups on nongrocery items
such as hardware and paper products.
A jewelry store,especially one that
makes much of its own jewelry,has
a relatively low number of sales each
week and will therefore have much
higher markups.
Markup Based on
Cost/Selling Price
Video
to Compute the Selling Price Based on Cost
1. Multiply the cost by the markup percent to get the dollar markup.
2. Add the dollar markup to the cost to get the selling price.
STEPS
8.3 These equations do not lend
themselves easily to the use of letters
instead of words.In speech,which
tends to be less exact,“markup”may
refer to the amount of dollar markup in
one sentence and then to the markup
percent in a subsequent sentence.
For Athletes’ World’s athletic shoes:
Dollar markup 5 Markup percent 3 Cost 5 0.80 3 $43.50 5 $34.80
Selling price 5 Cost 1 Dollar markup 5 $43.50 1 $34.80 5 $78.30
STEP 2
STEP 1
EXAMPLE A
Using markup based on cost, what are the dollar markup and the selling price for
merchandise that costs $60 and has a 35% markup?
Dollar markup 5 Markup percent 3 Cost 5 0.35 3 $60 5 $21
Selling price 5 Cost 1 Dollar markup 5 $60 1 $21 5 $81
STEP 2
STEP 1
COMPUTING SELLING PRICE DIRECTLY FROM COST
When you know the cost and markup percent (based on cost), you can compute the
selling price directly, without computing the dollar markup.
142 Part 2 Percentage Applications
to Compute the Selling Price Directly from the Cost
1. Add the markup percent to 100%.
2. Multiply this sum by the cost to get the selling price.
STEPS
EXAMPLE B
What is the selling price of an item that has a cost of $250 and a markup percent of 40%
based on cost?
100% 1 Markup percent 5 100% 1 40% 5 140%
Selling price 5 (100% 1 Markup percent) 3 Cost 5 1.40 3 $250 5 $350
STEP 2
STEP 1
COMPUTING COST DIRECTLY FROM SELLING PRICE
Likewise, you can use the reverse procedure to compute the cost directly from the selling
price and the markup percent (based on cost), without computing the dollar markup.
to Compute the Cost Directly from the Selling Price
1. Add the markup percent to 100%.
2. Divide the selling price by this sum to get the cost.
STEPS
EXAMPLE C
The selling price of a pair of shoes is $75. The markup percent based on cost is 25%.
Find the cost.
100% 1 Markup percent 5 100% 1 25% 5 125%
Cost 5 Selling price 4 (100% 1 Markup percent) 5 $75 4 1.25 5 $60
You can always check your work in markup problems.
Cost is $60, and markup percent is 25%.
Dollar markup 5 Cost 3 Markup percent 5 $60 3 0.25 5 $15
Selling Price 5 Cost 1 Dollar markup 5 $60 1 $15 5 $75
It checks!
STEP 2
STEP 1
Compute the required values when the markup percent is based on cost.
a. Cost 5 $1,240; Markup percent 5 40% Dollar markup 5 0.40 3 $1,240 5 $496
Find dollar markup, and then find selling price. Selling price 5 $1,240 1 $496 5 $1,736
b. Cost 5 $330; Markup percent 5 50% 100% 1 Markup percent 5 100% 1 50% 5 150%
Find 100% 1 Markup percent, and then find selling price directly. Selling price 5 1.50 3 $330 5 $495
c. Selling price 5 $780; Markup percent 5 25% 100% 1 Markup percent 5 100% 1 25% 5 125%
Find 100% 1 Markup percent, and then find cost directly. Cost 5 $780 4 1.25 5 $624
✔
CONCEPT CHECK 8.2
In the illustration for Athletes’ World, the accountant determined that the markup per-
cent needed to be 80% of cost, which meant that the selling price needed to be $78.30.
However, management may want to price the shoes at $79.95. Now, the markup is no
longer 80% of cost. The markup percent based on cost can be computed in two steps.
Chapter 8 Markup 143
Computing Markup Percent Based on Cost
Compute markup percent based
on cost.
3
Learning Objective
to Compute the Markup Percent Based on Cost
1. Subtract the cost from the selling price to get the dollar markup.
2. Divide the dollar markup by the cost to get the markup percent.
STEPS
© TED S. WARREN/ASSOCIATED PRESS
For the athletic shoes from Athletes’ World, priced at $79.95:
Dollar markup 5 Selling price 2 Cost 5 $79.95 2 $43.50 5 $36.45
Markup percent 5 Dollar markup 4 Cost 5 $36.45 4 $43.50 5 0.838,
or 83.8% (rounded to one decimal place)
STEP 2
STEP 1
EXAMPLE D
What is the markup percent based on cost when the selling price is $120 and the cost
is $80?
Dollar markup 5 Selling price 2 Cost 5 $120 2 $80 5 $40
Markup percent 5 Dollar markup 4 Cost 5 $40 4 $80 5 0.50, or 50%
STEP 2
STEP 1
EXAMPLE E
What is the markup percent based on cost when the dollar markup is already known to
be $30 and the cost is $75? (Step 1 is not necessary.)
Markup percent 5 Dollar markup 4 Cost 5 $30 4 $75 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 cost. Markup percent 5 $960 4 $1,600 5 0.60, or 60%
COMPLETE ASSIGNMENT 8.1.
✔
CONCEPT CHECK 8.3