132 ChAPTER 5 • USING EQUATIONS TO SOLVE BUSINESS PROBLEMS
EXAMPLE10
WRITING
EQUATIONS
For the following statements, underline the key words and translate into equations.
a. A number decreased by
14
is
23
.
b.
8
less than
3D
leaves
19
.
SolutionStrategy
Key Words Equation
a. A number decreased by
14
is
23
.
X−14 =23
8
3D
4
V
N
X
tryitexerciSe 10
For the following statements, underline the key words and translate into equations.
a. What number increased by
32
yields
125
?
b.
21
less than twice
C
gives
9
.
5
6
3
25
G
12
C
tryitexerciSe 9
For the following statements, underline the key words and translate into expressions.
a. The sum of twice
E
and
9
b.
6
times
N
divided by
Z
8
X
44
R
A
B
REviEw ExERciSES
Solve the following equations for the unknown and prove your solutions.
21K=63
Complete worked-out
5
SECTION I
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4
N
X
SECTION I • SOLVING BASIC EQUATIONS 133
10.
C
−3=10 11.
25A−11 =64
12.
R
+33 =84
13.
5(2S+1) =35
14.
C+5=26 −2C
15.
12(2D−4) =72
16.
14V+5−5V=4(V+5)
17.
Q+20 =3(9 −2Q)
For the following statements, underline the key words and translate into expressions.
18. 5 times G divided by R 19. The sum of
5
times
F
and
33
20.
6
less than one-fourth of
C
21.
550
more than the product of
H
and
P
22.
T
times
B
times
9
23. The difference of
8Y
and
128
24.
7
times the quantity of
X
and
7
25.
40
more than
3
4
of
B
For the following statements, underline the key words and translate into equations.
26. A number increased by
24
is
35
. 27. A number totals
5
times
B
and
C
.
X+24 =35
X=5B+C
12
33
R
4
5
2
40
BUSiNESS DEciSiON: GROUPiNG SymBOlS
32. 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 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.
the equations in Exercises 1–17 in
words.
Complete worked-out solutions for
Exercises 7–17 appear in Appendix B.
85461_ch05_hr_123-153.indd 133 9/23/15 4:37 PM
50Y=375
L
140 ChAPTER 5 • USING EQUATIONS TO SOLVE BUSINESS PROBLEMS
REviEw ExERciSES
Set up and solve equations for the following business situations.
1. Kathy and Karen work in a boutique. During a sale, Kathy sold eight fewer dresses than
Karen did. If together they sold
86
dresses, how many did each sell?
K
aren =X
K
athy =X−8
X
+
X
−
8
=
86
2X−8=86
+8 +8
2X=94
2X
2 =
94
2
X=47 Karen’s sales
X−8=47 −8=39 Kathy’s sales
2. One-fifth of the employees of Delta Industries, Inc., work in the Southeastern region. If the
company employs 252 workers in that region, what is the total number of employees working
for the company?
3. Walter’s salary this year is
$23,400
. If this is
$1,700
more than he made last year, what was his
salary last year?
4. The Book Nook makes four times as much revenue on paperback books as on hardcover books.
If last month’s sales totaled
$124,300
, how much was sold of each type book?
5. An online store sells two types of speaker docks for smartphones. The higher-priced speaker
dock sells for
$190
and the lower-priced speaker dock sells for
$80
. Last week the store sold
three times as many lower-priced speaker docks as higher-priced speaker docks. Combined
sales totaled
$3,440
. How many of each did it sell?
6. You are moving to a new home and have rented a truck to assist you with the move. Trailside
Truck Rentals charges
$39.95
per day plus
68
cents per mile. You will need the truck for
3days and will travel
460
miles. If you have budgeted
$400
for the truck rental, will this
amount be sufficient to cover the cost?
7. Kid’s Kingdom, a retail toy chain, placed a seasonal order for stuffed animals from Stuffed
Stuff, a distributor. Large animals cost
$20
, and small ones cost
$14
.
a. If the total cost of the order was
$7,320
for
450
pieces, how many of each size were ordered?
b. What was the dollar amount of each size ordered?
in the digital delivery of music which, in
turn, led phone makers to incorporate
music capabilities into their products.
Tap Magazine/Getty Images
5
SECTION II
8. PC Solutions sells regular keyboards for
$84
and wireless keyboards for
$105
. 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?
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 amounts to
$115,000
, how much will each person receive?
10. Pitt’s Pit Stop sold
$15,496.50
worth of gasoline yesterday. Regular sold for
$3.30
a gallon and
premium sold for
$3.45
a gallon. If the station sold
380
more gallons of regular than premium,
a. How many gallons of each type of gasoline were sold?
b. If the profit on regular gas is
$0.15
per gallon and on premium is
$0.18
per gallon, what
was the station’s total profit?
11. Yesterday Tween Teen 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?
12. You are the administrator of an annual essay contest scholarship fund. This year a
$48,000
college scholarship is being divided between the top two contestants so that the winner receives
three times as much as the runner-up. How much will each contestant receive?
13. The Cookie Monster 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?
b. What dollar amount of each type was sold?
TEAChING TIP
Review Exercise 9 is particularly
challenging because it involves
SECTION II • USING EQUATIONS TO SOLVE BUSINESS-RELATEd WORd PROBLEMS 141
142 ChAPTER 5 • USING EQUATIONS TO SOLVE BUSINESS PROBLEMS
14. If a
48
-piece set of stainless steel flatware costs
$124.80
at Bed Bath & Beyond, what is
thecost per piece?
15. The U.S. Congress has a total of
535
members. If the number of representatives is
65
less than
fivetimes the number of senators, how many senators and how many representatives are in Congress?
16. One-ninth of Polymer Plastics’ sales are made in New England. If New England sales amount
to
$600,000
, what are the total sales of the company?
1,000
20,000
50,000
17. You are the shipping manager for World Imports. Calculate the total cost to ship an order of
glassware weighing
1,860
pounds if the breakdown is
$0.04
per pound for packing,
$0.02
perpound for insurance,
$0.13
per pound for transportation, and
$132.40
for the crate.
18. Scott Mason purchased a
4
-unit apartment building as an investment before he retired. From the
rent he collects each month, Scott 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.
19. You are the facilities director of the Carnival 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?
Use ratio and proportion to solve the following business situations.
20. If a bulk order of
1,600
blouses costs
$41,600
, how much would
2,000
blouses cost?
21. At Fancy 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?
and related items, bath items,and
kitchen textiles) and home furnishings,
including kitchen and tabletop items,
stores exceeding
80,000
square feet.
Source: Based on Bed, Bath & Beyond website
85461_ch05_hr_123-153.indd 142 9/23/15 4:37 PM
22. A local FedEx Office store has a press that can print
5,800
brochures per hour. How many can
be printed during a
31
4
-hour run?
23. A recipe for turkey stuffing calls for three eggs for every
1
2
1
2
ounces of corn bread. If a dinner
party requires
8
7
1
2
ounces of corn bread for stuffing, how many eggs should be used?
24. An architect uses a scale of
3
4
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?
25. Following a recent election, it was reported that
300,000
people applied for
7,000
available jobs in the new president’s administration. At that rate, on average, how many
people had applied for each job? Round to the nearest whole person.
26. If auto insurance costs
$6.52
per
$1,000
of coverage, what is the cost to insure a car valued at
$17,500
?
27. Blue Sky International 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?
28. 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?
b. If Lazy Lawn costs
$1.19
for a
32
-ounce bag, what is the total cost to fertilize the lawn?
29. You have just been hired as advertising manager of The Daily Chronicle, a not-very-successful
newspaper. In the past, The Chronicle contained one-half advertising and one-half news stories.
Current industry research indicates a newspaper must have three times as much advertising as
news stories to make money. In addition, the advertising must be divided in the following ratio:
5
to
3
to
1
, retail advertising to national advertising to classified advertising. The Chronicle is
typically 48 pages in length.
a. How many pages should be advertising, and how many should be news stories?
FedEx office (formerly FedEx Kinko’s
and earlier simply Kinko’s) is a chain
of stores that provides a retail outlet
The primary clientele consists
of small business and home office
clients. There are more than 2,000
competitors include The UPS Store,
OfficeMax, Alpha Graphics, Staples,
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144 ChAPTER 5 • USING EQUATIONS TO SOLVE BUSINESS PROBLEMS
b. Based on the industry ratios, how should the pages be divided among the three types of
advertising?
c. After you made the changes in the advertising distributions ratios, your newspaper began
making a profit—for the first time in years. If last year’s total advertising revenue was
$810,000
, how much was earned by each type of advertising?
d. When you accepted the job of advertising manager, in addition to your salary, you were
promised a
1
50
share of each year’s revenue from retail and classified advertising and a
1
75
share for national. What bonus will you receive for last year’s sales?
BUSiNESS DEciSiON: HElPiNG caR maNUfactURERS—SaviNG
tHE PlaNEt!
30. In a move to provide additional sales for U.S. car manufacturers, the White House announced
the purchase of
17,600
new fuel-efficient vehicles for the federal fleet. The new fleet, which
includes
2,500
hybrid sedans, will cost
$285
million.
As an accountant in the White House Budget Office (WHBO), you have been asked to calcu-
late the following:
a. If each hybrid vehicle will have an average cost of
$24,000
, what will be the average cost
per non-hybrid vehicle? Round to the nearest whole dollar.
b. Furthermore, the White House said that by replacing less efficient vehicles, the government
will reduce gasoline consumption by
1.3
million gallons per year and prevent
26
million
pounds of carbon dioxide from entering the atmosphere. On average, how many gallons
of gasoline and how many pounds of carbon dioxide will be “saved” per year per vehicle?
Round to the nearest whole gallon and whole pound.
While retail advertising revenue has
Ronda Churchill/Bloomberg/Getty Images
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