Proof:
13 1 11 5 24
24 5 24
Proof:
21 2 16 5 5
555
Proof:
90 1 35 5 125
125 5 125
Proof:
70 2 58 5 12
12 5 12
Proof:
21(3) 5 63
63 5 63
2. C 2 16 5
5
1 16 1 16
C
5 21
3. S 1 35 5 125
235 235
S
5 90
4. M 2 58 5 12
1 58 1 58
M
5 70
5. 21K 5 63
21K
63
5
21
21
K53
L
58
5
L
(5) 5 8(5)
5
L 5 40
9. 6G 1 5 5 29
25 25
6G
5 24
6G
24
5
6
6
G54
8.
40
58
5
858
Proof:
6(4) 1 5 5 29
24 1 5 5 29
29 5 29
Proof:
1
Proof: 50a7 b 5 375
2
375 5 375
Proof: 135
5 45
3
45 5 45
CHAPTER 5—SECTION I
Z
5 45
3
Z
(3) 5 45(3)
3
Z 5 135
|
7. 50Y 5 375
50Y
375
5
50
50
1
Y5 7
2
6.
REVIEW EXERCISES
1. B 1 11 5 24
211 211
B
5 13
T5-1
14.
C 1 5 5 26 2 2C
1 2C
1 2C
3C 1 5 5 26
60
2 5 5 15
3
20 2 5 5 15
15 5 15
255
⫹ 33 ⫽ 84
5
51 ⫹ 33 ⫽ 84
84 ⫽ 84
42⫹ 52⫽
Proof: 3141
3(4(4)
1 5) 63
5 63
3116
⫹ 52⫽
3(16
1 5) 63
5 63
31212⫽
3(21) 63
5 63
63 63
⫽ 63
⫽ 63
Proof:
32⫺ 11
Proof: 25125(3)
2⫽
11 64
5 64
75 ⫺
75 11
2⫽
11 64
5 64
64 64
⫽ 64
64 ⫽
Proof:
|
CHAPTER 5—SECTION I
3C 1 5 5 26 3C
21 Proof:
5
25 25 3
3 7 1 5 5 26 2 2(7)
12 5 26 2 14
3C 5 21 C 5 7
12 5 12
48
12X
5
12
12
X54
R
(5) 5 51(5)
5
R 5 255
12. R
1 33 5 84
5
2 33 2 33
R
5 51
5
13. 3(4X 1 5) 5 63
12X 1 15 5 63
2 15 2 15
12X
5 48
25A
75
5
25
25
A53
D
(3) 5 20(3)
3
D 5 60
REVIEW EXERCISES
11. 25A 2 11 5 64
1 11 1 11
25A
5 75
10. D
2 5 5 15
3
15 15
D
5 20
3
T5-2
T5-3
REVIEW EXERCISES | CHAPTER 5—SECTION I
For the following statements, underline the key words and translate into expressions:
18. 5 times G divided by R
5G
R
20. 6 less than one-fourth of C
1
C26
4
22. T times B times 9
9TB
24. 7 times the quantity of X and 7
7(X 1 7)
19. The sum of 5 times F and 33
5F 1 33
21. 550 more than the product of H and P
HP 1 550
23. The difference of 8Y and 128
8Y 2 128
25. 40 more than
3
B 1 40
4
3
of B
4
T5-4
REVIEW EXERCISES | CHAPTER 5—SECTION I
For the following statements, underline the key words and translate into equations:
26. A number increased by 24 is 35.
X 1 24 5 35
28. 12 less than 4G leaves 33.
4G 2 12 5 33
27. A number totals 5 times B and C.
X 5 5B 1 C
29. The cost of R at $5.75 each is $28.75.
$5.75R 5 $28.75
30. Cost per person is the total cost divided by the number of persons.
C5
T
N
31. 4 more than 5 times a number, plus 2 times that number, is that number
increased by 40.
5X 1 4 1 2X 5 X 1 40
BUSINESS DECISION
|
CHAPTER 5—SECTION I
X 5 150
X 5 6(25)
X 5 6(2 1 23)
X 5 6(2 1 [18 1 9 2 4])
X 5 6(2 1 [3{6} 1 9 2 4])
X 5 6(2 1 [3{9 2 3} 1 {8 1 1} 2 4])
X 5 6(2 1 [3 {9 2 3} 1 {8 1 1} 2 4])
32. In algebra, grouping symbols are used to arrange numbers, variables, and operations.
In this chapter you learned to use the grouping symbols known as parentheses ( ). In
addition to parentheses, other symbols used in algebra for grouping are brackets [ ]
and braces { }. When solving equations with multiple grouping symbols, always start
with the innermost symbols, and work to the outside.
In business, you may encounter situations that require you to set up equations
with more than just parentheses. For practice, solve the following equation.
GROUPING SYMBOLS
T5-5
T5-6
REVIEW EXERCISES | CHAPTER 5—SECTION I I
Set up and solve equations for the following business situations:
1. Kathy and Karen work in a boutique. During a sale, Kathy sold eight less dresses than
Karen. If together they sold 86 dresses, how many did each sell?
Karen 5 X
Kathy 5 X 2 8
X 1 X 2 8 5 86
2X 2 8 5 86
18 18
2X
5 94
2X
94
5
2
2
X 5 47 Karen’s sales
X 2 8 5 47 2 8 5 39 Kathy’s sales
2. One-fifth of the employees of Action Hydraulics Corporation work in the Midwest
region. If the company employs 252 workers in that region, what is the total number
of employees working for Consolidated?
1
X 5 252
Total employees 5 X
5
1
(5) X 5 252(5)
5
X 5 1,260 Total employees
3. Larry’s salary this year is $23,400. If this is $1,700 more than he made last year, what
was his salary last year?
S 5 Larry’s salary last year
S 1 $1,700 5 $23,400
S 5 $21,000 Last year’s salary
4. Sylvia’s Bookstore makes four times as much money in paperback books as in hardcover
books. If last month’s sales totaled $124,300, how much was sold of each type book?
Hardcover 5 X
X 1 4X 5 124,300
X 5 $24,860 Hardcovers
Paperback 5 4X
5X 5 124,300
5X
124,300
5
5
5
4X 5 $99,440 Paperbacks
T5-7
REVIEW EXERCISES | CHAPTER 5—SECTION I I
5. The Winslow Desk Company production line made a total of 33 desks last week. If
they made half as many executive desks as regular desks, how many executive desks
did they make?
X
X
X 1 5 33
5 Executive desks
X 5 Regular desks
2
2
22
X
3
5 Executive desks
X 5 33
5 11 Executive desks
2
2
2
2 3
2
a b X 5 33a b
3 2
3
X 5 22 Regular desks
6. Jason’s weekly salary is $25 less than twice David’s salary. If together their salaries
total $1,425, what is David’s weekly salary?
Let D 5 David’s weekly salary
D 1 2D 2 25 5 1,425
2D 2 25 5 Jason’s weekly salary
3D 2 25 5 1,425
3D 5 1,425 1 25
3D 5 1,450
3D
1,450
5
3
3
D 5 $483.33 David’s weekly
salary
7. Toy World, a retail toy chain, placed a seasonal order for stuffed animals from a
distributor. Large animals cost $20.00 and small ones cost $14.00.
a. If the total cost of the order was $7,320 for 450 pieces, how many of each size
were ordered?
Large size 5 X
20X 1 14(450 2 X) 5 7,320
Small size 5 450 2 X 20X 1 6,300 2 14X 5 7,320
6X 5 1,020
X 5 170 Large size
450 2 X 5 280 Small size
b. What was the dollar amount of each size ordered?
Large size 5 $20(170) 5 $3,400
Small size 5 $14(280) 5 $3,920
T5-8
REVIEW EXERCISES | CHAPTER 5—SECTION I I
8. Robbins and Bryant invested $89,600 in a business. If Bryant invested three times as
much as Robbins, how much did each invest?
Robbins 5 X
X 1 3X 5 89,600
X 5 $22,400 Robbins’ investment
Bryant 5 3X
4X 5 89,600
3X 5 $67,200 Bryant’s investment
4X
89,600
5
4
4
9. An estate is to be distributed among a wife, three children, and two grandchildren.
The children will each receive three times as much as each grandchild, and the wife
will receive four times as much as each child. If the estate amounted to $115,000, how
much will each person receive?
Grand- 5 X
2X 1 3(3X) 1 4(3X) 5 115,000
X 5 $5,000 5 Each grandchild
child’s share
Child 5 3X
2X 1 9X 1 12X 5 115,000
3X 5 $15,000 5 Each child’s
share
23X
115,000
5
Wife 5 4(3X)
4(3X) 5 $60,000 5 Wife’s share
23
23
10. Yesterday, Town and Country Fashions had seven less than three-fourths of its sales
transactions paid for by credit cards. If 209 transactions were charged, how many
total transactions took place?
3
X 2 7 5 209
Total transactions 5 X
4
3
3
Charge cards 5 X 2 7
X 5 216
4
4
X 5 288 Total transactions
11. The deluxe model of a KitchenAid oven costs $46 more than twice the cost of the
standard model. If together they cost $1,234, what is the cost of each model?
Standard oven 5 X
X 1 2X 1 46 5 1,234
Deluxe oven 5 2X 1 46
3X 1 46 5 1,234
3X 5 1,188
X 5 $396 Cost of standard oven
2X 1 46 5 $838 Cost of deluxe oven
T5-9
REVIEW EXERCISES | CHAPTER 5—SECTION I I
12. PC Solutions sells regular keyboards for $84.00 and wireless keyboards for $105.00.
Last week the store sold three times as many regular keyboards as wireless. If total
keyboard sales were $4,998, how many of each type were sold?
Wireless keyboards 5 X
105X 1 84(3X) 5 4,998
Regular keyboards 5 3X
105X 1 252X 5 4,998
357X 5 4,998
X 5 14 Wireless keyboards
3X 5 42 Regular keyboards
13. The Michigan plant of DynoTech Industries is four times as old as the Ohio plant.
If the difference in the ages of the two plants is 9 years, what is the age of each?
Ohio plant 5 X
4X 2 X 5 9
Michigan plant 5 4X
3X 5 9
X 5 3 Age of Ohio plant
4X 5 12 Age of Michigan plant
14. Captain Cookie sells oatmeal cookies for $1.30 per pound and peanut butter cookies
for $1.60 per pound.
a. If total cookie sales last week amounted to 530 pounds, valued at $755, how
many pounds of each type of cookie were sold?
Peanut butter 5 X
1.60X 1 1.30(530 2 X) 5 755
X 5 220 Pounds of peanut
butter cookies
Oatmeal 5 530 2 X
1.60X 1 689 2 1.30X 5 755
530 2 X 5 310 Pounds of oatmeal
.30X 1 689 5 755
cookies
.30X 5 66
b. What dollar amount of each type was sold?
$1.60(220) 5 $352 Sales of peanut butter cookies
$1.30(310) 5 $403 Sales of oatmeal cookies
REVIEW EXERCISES
|
CHAPTER 5—SECTION II
17. If a 48-piece set of stainless steel flatware costs $124.80 at Crate and Barrel, what is
the cost per piece?
124.80
X5
Cost per piece 5 X 48X 5 124.80
48
48X
124.80
X 5 $2.60 Cost per piece
5
48
48
16. Marcus Welby paid the same price for each of 8 tickets to a concert. If he paid a
total of $170, what was the price of each ticket?
P 5 price per ticket
8P 5 $170
8P
170
5
8
8
P 5 $21.25 Per ticket
15. One-ninth of Superior Plastics’ sales are made in New England. If New England sales
amount to $600,000, what are the total sales of the company?
1
X 5 600,000
Total sales 5 X
9
1
New England sales 5 X
X 5 $5,400,000 Total sales
9
T5-10
T5-11
REVIEW EXERCISES | CHAPTER 5—SECTION I I
18. What is the total cost to ship an order weighing 1,860 pounds, if the breakdown is
$.04 per pound for packing, $.02 per pound for insurance, $.13 per pound for
transportation, and $132.40 for the crate?
Total cost 5 X X 5 .04(1,860) 1 .02(1,860) 1 .13(1,860) 1 132.40
X 5 74.40 1 37.20 1 241.80 1 132.40
X 5 $485.80 Total cost to ship order
19. Jorge Ortiz purchased a 4-unit apartment building as an investment before he retired.
From the rent he collects each month, Jorge pays out $600 for expenses. How much
rent must he charge for each of the 4 apartments if he wants to make $500 profit each
month? The amount of rent is the same for each of the apartments.
Let R 5 Amount of rent to charge each month
4R 2 600 5 500
4R 5 1,100
1,100
4R
5
4
4
R 5 $275 Rent for each apartment
20. You are the facilities director of a local shopping mall. You have been asked to rope
off a rectangular section of the parking lot for a car show next weekend. The area to
be roped off is 250 feet long by 300 feet wide. Rubber traffic cones are to be placed
every 25 feet around the lot. How many cones are needed?
The perimeter around the rectangular area is:
(2 3 250) 1 (2 3 300) 5 500 1 600 5 1,100 feet
Let X 5 Number of cones needed
1,100
X5
5 44 Cones to be placed around the area
25
REVIEW EXERCISES
|
CHAPTER 5—SECTION II
4,600X 5 370(9,660)
4,600X 5 3,574,200
X 5 $777 Interest on $9,660 loan
23. If auto insurance costs $6.52 per $1,000 of coverage, what is the cost to insure a car
valued at $17,500?
1,000X 5 6.52(17,500)
X
6.52
5
1,000X 5 114,100
1,000
17,500
X 5 $114.10 Cost of insurance
22. At Rainbow Fruit Distributors, Inc., the ratio of fruits to vegetables sold is 5 to 3. If
1,848 pounds of vegetables are sold, how many pounds of fruit are sold?
3X 5 5(1,848)
5
X
5
3X 5 9,240
3
1,848
X 5 3,080 Pounds of fruit
4,600
9,660
5
370
X
21. If the interest on a $4,600 loan is $370, what would be the interest on a loan of $9,660?
Use ratio and proportion to solve the following business situations:
T5-12
REVIEW EXERCISES
|
CHAPTER 5—SECTION II
26. If a car goes 48 miles per hour at 3,300 rpm (revolutions per minute) of the engine,
how fast will it go at 4,000 rpm in the same gear?
3,300X 5 48(4,000)
48
X
5
3,300X 5 192,000
3,300
4,000
X 5 58.2 Miles per hour at 4,000 RPM
25. An architect uses a scale of 34 inch to represent 1 foot on a blueprint for a building. If
the east wall of the building is 36 feet long, how long will the line be on the blueprint?
3
3
X
X 5 (36)
4
5
4
1
36
X 5 27 Inches on the blueprint
24. A recipe for turkey stuffing calls for three eggs for every 12 12 ounces of corn bread.
If a dinner party requires 87 12 ounces of corn bread for stuffing, how many eggs should
be used?
X
1
3
1
5
12 X 5 3a87 b
1
1
2
2
12
87
2
2
1
1
12 X 5 262
2
2
X 5 21 Eggs needed for recipe
T5-13
T5-14
REVIEW EXERCISES | CHAPTER 5—SECTION I I
27. KwikPrint has a press that can print 5,800 brochures per hour. How many can be
printed during a 3 14-hour run?
5,800
1
X
X 5 5,800 a 3 b
5
1
4
1
3
4
1
X 5 18,850 Brochures printed in 3 hours
4
28. A local airport handles passenger to cargo traffic in a ratio of 8 to 5. If 45 cargo planes
landed yesterday, how many passenger flights came in?
8
X
5X 5 80(45)
5
5X 5 360
5
45
X 5 72 Passenger flights
29. Eighty ounces of Lazy Lawn fertilizer covers 1,250 square feet of lawn.
a. How many ounces would be required to cover a 4,000-square-foot lawn?
X
80
1,250X 5 80(4,000)
5
1,250X 5 320,000
1,250
4,000
X 5 256 Ounces needed to cover 4,000 sq ft
b. If Lazy Lawn costs $1.19 for a 32-ounce bag, what is the total cost to fertilize the
lawn?
32X 5 1.19(256)
1.19
X
5
32X 5 304.64
32
256
X 5 $9.52 Total cost
T5-15
BUSINESS DECISION | CHAPTER 5—SECTION I I
THE ASPECT RATIO
30. Wide-screen televisions have screens that are shaped like those in a movie theater.
They are known as a 16 : 9 aspect ratio screen. This means that the ratio of the width
to the height is in the ratio of 16 to 9. In most cases, the cabinet dimensions are the
same ratio. More conventional TVs have screens with an aspect ratio of 4 : 3, width
to height.
You are a salesperson for Galaxy Electronics, an upscale audio/video equipment
store. Customers switching from conventional to wide-screen models often have questions about the size of set that will fit in their wall units or shelves that previously held
the conventional 4 : 3 sets.
a. James Yamamoto, one of your customers, has a conventional TV that is 36
inches wide. What is the height of that TV?
4
36
Width
5 5
Height
3
X
4X 5 3(36)
X 5 27 Inches
b. If James purchases a wide-screen TV with a cabinet 36 inches wide, what would
be the height of that set? Round to the nearest tenth of an inch.
Width
16
36
5
5
Height
9
X
16X 5 9(36)
X 5 20.3 Inches
c. As an astute salesperson, you know that wide-screen TV cabinets require less
height than conventional models, so you often suggest that there may be room
for a larger set in the current space. If the next larger size wide-screen is 26
inches high, how much shelf space, in width, would be required? Round to a
tenth.
Width
16
X
5
5
Height
9
26
9X 5 16(26)
X 5 46.2 Inches
d. As it turns out, there was room for the larger set, and you made the sale! Your
1
commission amounts to 25
of your sales revenue. If the small set is priced at
$3,500 and the larger one is $4,800, how much extra commission did you earn by
suggesting the larger size?
4,800
23,500
1,300
1,300 3
1
5 $52
25