Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges
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C (27 points) Write the following numbers in columns, and then add. (3 points for each correct answer)
38.
3.84, 42.81, 747.114 39. 0.7323, 4.084, 17.42 40. 15.4, 32.574, 9.51, 74.0822
64 Part 1 Fundamental Review
Assignment 3.1 Continued
47. 0.734 48. 0.04264 49. 26.04 50. 0.7212
0.37
0
0.00497 8.625 0.034
0
51. 6.1 52. 804.07 53. 3.2525 54. 708.932
2.418 167.1
0
2.843
0
419.058
3.84 0.7323 15.4
42.81 4.084 32.574
747.114 17.42. .. 9.51
793.764 22.2363
74.0822
131.5662
55. 0.365 56. 4.37 57. 7.624 58. 5.6976
0.189 1.9055 5.947 4.6913
0.176 2.4645 1.677 1.0063
Score for D (36)
D (36 points) Subtract the following. (3 points for each correct answer)
3.682 636.97 0.4095 289.874
0.364 0.03767 17.415 0.6872
44. 337.51, 6.1761, 16.078 45. 36.7, 208.51, 3.992 46. 0.592, 1.82, 0.774, 6.5
41. 24.78, 71.402, 8.3176 42. 7.911, 64.3075, 288.69 43. 6.4, 3.211, 12.6, 7.07
24.78 7.911 6.4
71.402 64.3075 3.211
8.3176 288.6900 12.6
104.4996 360.9085
07.070
29.281
337.51 36.7 0.592
6.1761 208.51 1.82
16.078
.
3.992
0.774
359.7641 249.202
6.5 0
9.686
Score for C (27)
Chapter 3 Decimals 65
Name
Date Score
5
Learning Objectives
6 7 8
Assignment 3.2: Multiplication and Division of Decimal Numbers
Name
Date Score
10 969 12 300 2 52000 2 8900
47 010
98 400 00 00000 17 3400
1253 600 $110.700 336 00000 $20.2300
$1,311.579 $338.52000
$1,311.58 $110.70 $338.52 $20.23
4 2884 2 6465 22 8562608 2 44812
75 0470 21 1720 57 1406520 00 0000
79.3354 23.8185 79.9969128
326 416
00
328.86412
79.3354 23.8185 79.9969128 328.86412
5. 107.21 6. 52.93 7. 285.70326 8. 816.04
0.74 0.45 0.28 0.403
Score for A (32)
B (24 points) Divide the following. Round monetary quotients to the nearest cent. Round nonmonetary
quotients to two decimal places. (4 points for each correct answer)
9. 10. 11.
1.2q$54.300
$ 45.25
0.36 q$6.7500
$ 18.75
7q$12.95
$ 1.85
00
0
$ 18.75
$ 45.25
$ 1.85
7 3 6 48
59 315 63
56 288 60
35 270 30
35 252 24
180 60
180 60
$1.85 $18.75 $45.25
A (32 points) Multiply the following. Round monetary products to the nearest cent. Do not round
nonmonetary products. (4 points for each correct answer)
1. $15.67 2. $24.60 3. $420.00 4. $57.80
83.7 . 4.5 0.806 0.35
12. 13. 14.
0.09q0.7888 0
8.764
0.11q0.6735 0
6.122
1.5q2.5 9 00
1.713
66 Part 1 Fundamental Review
Assignment 3.2 Continued
1.726
00
6.122
0
8.764
0
15 66 72
109 13 68
105 11 63
40 25 58
30 22 54
100 30 40
90 22 36
1.73 6.12 8.76
Score for B (24)
C (12 points) Multiply and/or divide by just moving the decimal point or by doing some simple multiplica-
tion/division and moving the decimal point. Round monetary answers to the nearest cent. Do not round
nonmonetary answers. (1 point for each correct answer)
15. 0.0625 1,000 21. $72.41 300
16. 50.708 100 22. $32.25 20
17. 0.047 10,000 23. $0.12 6,000
18. 763 100 24. $2.50 40
19. 6.32 10 25. $86.50 200
20. 27.469 1,000 26. $9,612 40
Score for C (12)
D (32 points) For each of the following problems, underline the estimate that is most nearly correct.
(2 points for each correct answer)
27.
0.077 0.52 (a) 4.0 (b) 0.4 (c) 0.04 (d) 0.004
28. 76.7 0.8477 (a) 0.064 (b) 0.64 (c) 6.4 (d) 64
29. 0.38 71.918 (a) 0.28 (b) 2.8 (c) 28 (d) 280
30. 0.00907 6.12 (a) 0.054 (b) 0.54 (c) 5.4 (d) 54
31. 0.0782 0.5503 (a) 0.0048 (b) 0.048 (c) 0.48 (d) 4.8
32. 0.0417 0.0957 (a) 0.04 (b) 0.004 (c) 0.0004 (d) 0.00004
33. 268.25 0.9175 (a) 27,000 (b) 2,700 (c) 270 (d) 27
34. 0.0487 0.0059 (a) 0.000003 (b) 0.00003 (c) 0.0003 (d) 0.003
35. 19.1 6104 (a) 120 (b) 1,200 (c) 12,000 (d) 120,000
36. 7.958 0.514 (a) 16 (b) 160 (c) 1,600 (d) 16,000
37. 3.575 893.12 (a) 0.004 (b) 0.04 (c) 0.4 (d) 4
38. 0.0614 0.00398 (a) 0.15 (b) 1.5 (c) 15 (d) 150
39. 8.397 7.12 (a) 0.12 (b) 1.2 (c) 12 (d) 120
40. 0.5379 0.591 (a) 900 (b) 90 (c) 9 (d) 0.9
41. 5.112 0.0692 (a) 70 (b) 7 (c) 0.7 (d) 0.07
42. 2.671 0.0926 (a) 300 (b) 30 (c) 3 (d) 0.3
Score for D (32)
$240.300.027469
$0.430.632
$100.007.63
$720.00470
$645.005,070.8
$21,723.0062.5
Chapter 3 Decimals 67
Assignment 3.3: Decimal Numbers in Business
Name
Date Score
A (36 points) Business Applications and Critical Thinking. Solve the following. Do not round your final
answers. (6 points for each correct answer)
3
Learning Objectives
4 5 6
1. Bob Jones had 24.75 feet of rope. He cut off a
piece 16.5 feet long. How much did he have
left?
2. Cho Jewelers had only 12.7 ounces of gold on
hand, so Mr. Cho bought 22.5 ounces more to
make Christmas items. He used 18.7 ounces for
gold rings. How much gold did he have left?
35.2
218.7
16.5
12.7
122.5
35.2
16.5 oz
24.75
16.5
8.25
8.25 ft
3. Judy Taylor reads meters for the gas and electric
company. She walked 3.6 miles on Monday;
3.7 miles on Tuesday, 2.9 miles on Wednesday,
3.25 miles on Thursday, and 3.4 miles on Fri-
day. What was her total distance for the week?
4. Four messenger service drivers need gasoline
for their cars. Individually, they buy 12.4, 8.9,
11.7, and 13.9 gallons. How much do they pur-
chase all together?
12.4
8.9
11.7
13.9
46.9
46.9 gal
3.6
3.7
2.9
3.25
1 3.4
16.85
16.85 mi
5. A retail customer owes a total of $226.54 on her
department store account. She visits the store to
return an item that cost $47.79. While there, she
buys two items that cost $55.88 and $67.50. What
is her new account balance at the store?
6. Parker Paving Co. delivered 6.2 tons of asphalt.
It used 4.7 tons for a driveway and 1.2 tons for a
walkway. How much asphalt was left?
Score for A (36)
1.5
21.2
0.3
6.2
24.7
1.5
0.3 t
$178.75
55.88
1 67.50
$302.13
$226.54
2 47.79
$178.75
$302.13
B (64 points) Business Applications and Critical Thinking. Solve the following business problems. Use short-
cuts where possible.If necessary, round answers to two decimal places. (8 points for each correct answer)
68 Part 1 Fundamental Review
Assignment 3.3 Continued
7. Bill Wells Hardware sells a large-diameter plas-
tic pipe for $0.17 per foot and copper pipe for
$1.32 per foot. How much will Katy Cruz save
by using plastic pipe if she needs 400 feet of
pipe?
8. Benoit Landscaping sent three truckloads of
topsoil to a job. The soil cost $28.50 per cubic
yard. Two trucks carried 7.25 cubic yards each;
the third carried 6.75 cubic yards. What was
the total cost of all the topsoil?
$605.63$460
9. Wholesale, 1,000 2-ounce plastic bottles cost
3.5 cents each, and 2,000 4-ounce bottles cost
4.5 cents each. What is the total cost of all
3,000 bottles?
10. Evelyn Haynes often used her motorcycle as a
delivery vehicle. One Monday, when regular
gasoline was priced at $4.499 per gallon, Evelyn
bought 2.62 gallons. The following Thursday,
regular gasoline prices rose to $4.799 per gallon
and she bought 2.87 gallons. What was the
total amount that Evelyn spent for gasoline
those two days?
$25.56
$125
11. Electrician Tom Stewart paid $95.50 for 500
feet of multistrand electrical wire. What was
the cost per foot for this particular wire?
12. A pizza chef has 24 pounds of flour on hand.
He needs 3.75 pounds of flour for one large
recipe of pizza dough. How many recipes can
he make with the flour on hand? (Round to the
nearest tenth.)
6.4 recipes
$0.19
Move decimal point 2 places right
$4.60 $460
$1.15
3 4
$4.60
$1.32
20.17
$1.15
7.25 $28.50
7.25
21.25
6.75 14250
21.25 5700
2850
5700000
$605.6250
3.5¢ $0.035 4.5¢ $0.045
$0.035 1,000 $35 $0.045 2,000 $90
$35 $90 $125
2.62 $4.499 $11.78738, or $11.79
2.87 $4.799 $13.77313, or
13.77
$25.56
$95.50 5 $19.10
Move decimal point 2 places left
$19.10 $0.191 or $0.19
6.4
2250
1500
1500
0
3.75.q24.00.0
13. Paint thinner costs $1.49 per gallon. How many
gallons can a painting contractor buy for $100?
(Round to the nearest tenth.)
14. Jackie Barner earns $22.60 per hour. How
many hours did she work during a partial day
for which her pay was $152.55?
6.75 hr67.1 gal
Score for B (64)
67.11
8 94
1060
1043
170
149
210
149
1.49.q100.00.00
6.75
135 60
16950
15820
11300
11300
0
22.60.q152.55.00
Word Problems
and Equations
Chapter 4 Word Problems and Equations 69
Learning Objectives
By studying this chapter and completing all assignments, you will be able to:
Use a systematic approach to solve word problems.
Apply formulas to solve rate, time, and distance problems.
Solve simple numerical equations.
Recognize numerical relationships in a series.
Do quick mental calculations through a process of rounding numbers.
4
1
Learning Objective
2
Learning Objective
3
Learning Objective
4
Learning Objective
5
Learning Objective
70 Part 1 Fundamental Review
Word Problems
VIDEO
to Solve Word Problems
1. Read the problem carefully.
2. Determine what is requested.
3. Determine the processes to use.
STEPS
We use these steps to solve the word problem in example A.
Read the problem carefully.
Determine what is requested: How much money would the company pay?
Determine the processes to use.
Add square yards in the three offices: 15 1 15 1 10 5 40.
Multiply the total square yards by the $10 per square yard cost: 40 3 $10 5 $400.
Subtract the $50 discount: $400 2 $50 5 $350.
Some word problems involve all four fundamental processes: addition, subtraction,
multiplication, and division.
EXAMPLE B
Phoebe Elias owns half of a small bakery. Last week she baked 6 cakes on Monday, 9 on
Tuesday, 11 on Wednesday, 8 on Thursday, and 6 on Friday. She sold all cakes for $9 each.
It cost Phoebe $5 to make each cake; the rest was her profit on each cake. Phoebe split her
profit evenly with her partner. How much did her partner receive from last week’s cakes?
Read the problem carefully.
Determine what is requested: How much money did Phoebe’s partner receive?
Determine the processes to use.
Add the cakes baked: 6 1 9 1 11 1 8 1 6 5 40.
Subtract the cost from the sales price: $9 2 $5 5 $4 profit per cake.
Multiply the number of cakes sold by the $4 profit per cake: 40 3 $4 5 $160.
Divide the total profit by 2: $160 4 2 5 $80 received by the partner.
STEP3
STEP 2
STEP 1
STEP 3
STEP 2
STEP 1
4.1 Note for students that in the mod-
ern business world many math-related
problems are presented in word form.
Solving Word Problems
Word problems in business are solved by using a three-step approach and applying simple
addition, subtraction, multiplication, and division.
EXAMPLE A
A company orders carpeting for three offices measuring 15 square yards, 15 square yards,
and 10 square yards, respectively. A carpet dealer sells the carpet for $10 a square yard
and gives a $50 discount when the sale is for three or more offices. How much would the
company pay to have the three offices carpeted?
15 sq yd 1 15 sq yd 1 10 sq yd 5 40 sq yd
40 sq yd 3 $10 5 $400 gross price
$400 2 $50 discount 5 $350 net price
1
Learning Objective
Use a systematic approach to solve
word problems.
Chapter 4 Word Problems and Equations 71
In some business word problems, you must compute how much is done in a given
amount of time at a specific speed. These rate, time, and distance problems are solved
with a simple formula: Rate (speed) 3 Time 5 Distance (amount done). If you are given
any two factors, it is easy, by formula, to find the third.
Rate 3 Time 5 Distance
Distance 4 Time 5 Rate
Distance 4 Rate 5 Time
EXAMPLE C
Jan traveled at 35 miles per hour for 5 hours. How far did Jan travel?
35 mph 3 5 hr 5 175 mi
(Rate 3 Time 5 Distance)
EXAMPLE D
Jan traveled 175 miles in 5 hours. How fast was Jan traveling?
175 mi 4 5 hr 5 35 mph
(Distance 4 Time 5 Rate)
EXAMPLE E
At 35 miles per hour, how long would it take Jan to travel a total of 175 miles?
175 mi 4 35 mph 5 5 hr
(Distance 4 Rate 5 Time)
Problem: Maria wants to upholster three chairs. Two chairs will require 4 yards of material each; the third will require
3 yards. One material costs $32 per yard; the other costs $15 per yard. What is the difference between the costs of the
two materials for upholstering the chairs?
Read the problem carefully.
Determine what is requested: Difference in cost between the two materials.
Determine the processes to use.
Add amount of material needed: 4 yd 1 4 yd 1 3 yd 5 11 yd.
Multiply amount of material needed by cost per yard—first material: 11 yd 3 $32 per yd 5 $352.
Multiply amount of material needed by cost per yard—second material: 11 yd 3 $15 per yd 5 $165.
Subtract cost between the two materials: $352 2 $165 5 $187 difference in cost.
✔
Summary of steps for solving word problems:
1. Read the problem carefully.
2. Determine what is requested.
3. Determine the processes to use.
CONCEPT CHECK 4.1
Solving Rate, Time, and Distance Problems
© JAMES BOULETTE/ISTOCK-
PHOTO INTERNATIONAL
Apply formulas to solve rate, time,
and distance problems.
2
Learning Objective
72 Part 1 Fundamental Review
EXAMPLE F
Jan and Ahmed start traveling toward each other from 300 miles apart. Jan is traveling at
35 miles per hour; Ahmed is traveling at 40 miles per hour. How much time will elapse
before they meet?
Distance 5 300 mi
Total rate 5 35 mph (Jan) 1 40 mph (Ahmed) 5 75 mph
300 mi 4 75 mph 5 4 hr
(Distance 4 Rate 5 Time)
EXAMPLE G
Jan and Ahmed start traveling toward each other from 300 miles apart. Jan is traveling at
35 miles per hour; Ahmed is traveling at 40 miles per hour. How much distance will Jan
travel before they meet?
Total rate 5 35 mph (Jan) 1 40 mph (Ahmed) 5 75 mph
Time 5 300 mi 4 75 mph 5 4 hr
Jan’s distance 5 35 mph (Jan’s Rate) 3 4 hr (Time) 5 140 mi
EXAMPLE H
Mary needs to type a term paper that will be 30 pages long. Each page contains about
200 words. If Mary can type 40 words per minute, how many minutes will it take her to
complete the paper?
Choose a formula: We know distance (amount done) and speed (rate). Therefore, we choose
the formula for time.
Distance (amount done) 4 Rate (speed) 5 Time
30 pages 3 200 words 5 6,000 words 4 40 wpm 5 150 min
EXAMPLE I
Flora also had a paper to type, but hers was 9,000 words in length. She was able to type it
in 150 minutes. How fast did she type?
Choose a formula: We know distance (amount done) and time. Therefore, we choose the for-
mula for rate.
Distance (amount done) 4 Time 5 Rate (speed)
9,000 words 4 150 min 5 60 wpm
EXAMPLE J
It is approximately 400 miles from San Francisco to Los Angeles. Roy’s friends tell him
that he can make the trip in 6 hours if he averages 60 miles per hour. Is this true?
Choose a formula: We know the rate and the time, so we choose the formula for distance.
Rate (speed) 3 Time 5 Distance (amount done)
60 mph 3 6 hr 5 360 mi
Can he get there in 6 hours? No.
Chapter 4 Word Problems and Equations 73
A numerical sentence in which both sides of an equal sign contain calculations is called
an equation. For example, five plus five equals twelve minus two (5 1 5 5 12 2 2) is an
equation, as is seven minus one equals thirty divided by five (7 2 1 5 30 4 5).
For an equation to be true, the numbers on the left of the equal sign must always
compute to the same answer as the numbers on the right of the equal sign. Moving a
number from one side of the equation to the other changes its sign. A plus sign will
change to minus; a minus sign will change to plus. A multiplication sign will change to
division; a division sign will change to multiplication.
Apply the appropriate formula to answer the following question: A machine that produces tor-
tillas at the Baja Restaurant can produce 200 tortillas per hour, or 1,600 tortillas in an 8-hour
day. A new machine can produce 3,000 tortillas in 6 hours. How many more tortillas per hour
can the new machine produce than the old one?
Distance (amount done) 4 Time 5 Rate
1,600 tortillas 4 8 hr 5 200 per hr
3,000 tortillas 4 6 hr 5 500 per hr
Difference: 500 2 200 5 300 more tortillas per hr
✔
The basic formulas:
a. Rate (speed) 3 Time 5 Distance (amount done)
If you know any two factors, you can find the third.
b. Distance (amount done) 4 Time 5 Rate (speed)
c. Distance (amount done) 4 Rate (speed) 5 Time
CONCEPT CHECK 4.2
Solving Simple Numerical Equations
EXAMPLE K Addition—Subtraction
6 1 4 1 5 5 17 2 2
Change the 2 2:
6 1 4 1 5 1 2 5 17
Now change the 1 5:
6 1 4 1 2 5 17 2 5
EXAMPLE L Multiplication—Division
3 3 8 5 48 4 2
Change the 4 2:
3 3 8 3 2 5 48
Now change the 3 8:
3 3 2 5 48 4 8
Solve simple numerical equations.
3
Learning Objective