CHAPTER
6
Percents and
Their Applications
in Business
PowerPoint Presentation by Charlie Cook
The University of West Alabama
© 2009 Cengage Learning. All rights reserved.
PERFORMANCE OBJECTIVES
Section I
Understanding and Converting Percents
6-1: Converting percents to decimals and decimals to percents
6-2: Converting percents to fractions and fractions to percents
Section II Using the Percentage Formula to Solve Business
Problems
6-3: Solving for the portion
6-4: Solving for the rate
6-5: Solving for the base
Section III Solving Other Business Problems Involving Percents
6-6: Determining rate of increase or decrease
6-7: Determining amounts in increase or decrease situations
6-8: Understanding and solving problems involving percentage points
© 2009 Cengage Learning. All rights reserved.
6–2
Understanding Equations
Formula
A mathematical representation of a fact, rule, principle, or other logical
relation in which letters represent number quantities.
Equation
A mathematical statement expressing a relationship of equality; usually
written as a series of symbols that are separated into left and right
sides and joined by an equal sign. X + 7 = 10 is an equation.
Expression
A mathematical operation or a quantity stated in symbolic form, not
containing an equal sign. X + 7 is an expression.
Constants
(Knowns)
The parts of an equation that are given. In equations, the knowns are
constants (numbers), which are quantities having a fixed value. In the
equation X + 7 = 10, 7 and 10 are the knowns or constants.
Terms
The knowns (constants) and unknowns (variables) of an equation. In
the equation X + 7 = 10, the terms are X, 7, and 10.
Solve an
Equation
The process of finding the numerical value of the unknown in an
equation.
© 2009 Cengage Learning. All rights reserved.
6–3
Understanding and Converting Percents
• percent
 A way of representing the parts of a whole. Percent
means per hundred or parts per hundred.
• percent sign
 The symbol, %, used to represent percents. For
example, 1 percent would be written 1%.
© 2009 Cengage Learning. All rights reserved.
6–4
Converting Percents to Decimals
© 2009 Cengage Learning. All rights reserved.
6–5
Converting Percents to Decimals Example
28%
.28
13.4%
.134
6½% = 6.5%
.065
.02%
.0002
© 2009 Cengage Learning. All rights reserved.
6–6
Converting Decimals to Percents
© 2009 Cengage Learning. All rights reserved.
6–7
Converting Decimals to Percents Example
3.5
350%
.34½
.345 = 34.5%
.00935
.935%
5.33
533%
© 2009 Cengage Learning. All rights reserved.
6–8
Converting Percents to Fractions
© 2009 Cengage Learning. All rights reserved.
6–9
Converting Percents to Fractions Example
5
1
5% 

100
20
37.5%  37
1
2
1
75
1
75
3





100
2
100
200
8
1
62 %  62
2
1
2
1
125
1
125
5





100
2
100
200
8
8
1
8
1
.8% 



10 100
1000
125
© 2009 Cengage Learning. All rights reserved.
6–10
Converting Percents to Fractions Example
(cont’d)
230
230% 
 2
100
30
100
 2
3
10
450
450% 
 4
100
50
100
 4
1
2
8
1
8
1
.8% 



10 100
1000
125
© 2009 Cengage Learning. All rights reserved.
6–11
Converting Fractions to Percents
3
 .75  75%
4
12
 2 52  2.4  240%
5
125
 1 14  1.25  125%
100
© 2009 Cengage Learning. All rights reserved.
6–12
Converting Fractions to Percents
3
 .75  75%
4
12
 2
5
2
5
 2.4  240%
125
 1
100
1
4
 1.25  125%
78
 3
24
4
© 2009 Cengage Learning. All rights reserved.
1
5
1
4
 3.25  325%
 4.2  420%
6–13
Using the Percentage Formula
to Solve Business Problems
• base
 The variable of the percentage formula that
represents 100%, or the whole thing.
• portion
 The variable of the percentage formula that
represents a part of the base.
• rate
 The variable of the percentage formula that defines
how much or what part the portion is of the base. The
rate is the variable with the percent sign.
© 2009 Cengage Learning. All rights reserved.
6–14
Steps for Solving Percentage Problems
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6–15
The Magic Triangle
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6–16
Sample Percentage Problems
• Maritza Torres owns 37% of a travel agency.
• If the total worth of the business is $160,000,
how much is Maritza’s share?
P  R  B  .37  160,000  59,200
© 2009 Cengage Learning. All rights reserved.
6–17
Sample Percentage Problems (cont’d)
• What is the sales tax in a state where the tax on
a purchase of $464 is $25.52?
P
25.52
R 

 .055  5.5%
B
464
© 2009 Cengage Learning. All rights reserved.
6–18
Sample Percentage Problems (cont’d)
• The Daily Times reports that 28% of its advertising is for
department stores.
• If the department store advertising amounts to $46,200,
what is the total advertising revenue of the newspaper?
P 46,220
B 
 165,000
R
.28
© 2009 Cengage Learning. All rights reserved.
6–19
Sample Percentage Problems (cont’d)
• Lisa Walden, a sales associate for a large company,
successfully makes the sale on 40% of her sales
presentations.
• If she made 25 presentations last week, how many sales
did she make?
P  R  B  .4  25  10
© 2009 Cengage Learning. All rights reserved.
6–20
Sample Percentage Problems (cont’d)
• A quality control process finds 17.2 defects for
every 8,600 units of production.
• What percent of the production is defective?
P
17.2
R 

 .002  0.2%
B
8,600
© 2009 Cengage Learning. All rights reserved.
6–21
Sample Percentage Problems (cont’d)
• The Bentley Bobcats have won 80% of their
basketball games. If they lost 4 games, how
many games have been played?
Won = 80%
Lost = 20%
P
4
B 

 20
R
.2
© 2009 Cengage Learning. All rights reserved.
6–22
Determining Rate of Increase or Decrease
Amount of change
Rate of Change 
Original amount
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6–23
Rate of Increase or Decrease Example
• Allied Plumbing sold 2,390 feet of 5/8-inch galvanized
pipe in July. If 2,558 feet were sold in August, what is
the percent increase in pipe footage sales?
P  Increase  2,558  2,390  168
B  Original Amount  2,390
P
168
R 

 .07  7%
B
2,390
© 2009 Cengage Learning. All rights reserved.
6–24
Rate of Increase or Decrease Example
• The supermarket price of yellow onions dropped from
$.59 per pound to $.45 per pound. What is the percent
decrease in the price of onions?
P  Decrease  $0.59  $0.49  $0.14
B  Original Amount  $0.59
P .14
R 
 .2373  23.73%
B .59
© 2009 Cengage Learning. All rights reserved.
6–25
Determining the New Amount
After a Percent Change
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6–26
Determining the New Amount After
a Percent Change Example
• Economists predict that next year housing prices
will drop by 4%. This year’s price for an average
house is $110,000. What will the average price
of a house be next year?
Rate  100%  4%  96%
Base  Original Amount  110,000
P  R  B  .96  110,000  105,600
© 2009 Cengage Learning. All rights reserved.
6–27
Determining the Original Amount
Before a Percent Change
© 2009 Cengage Learning. All rights reserved.
6–28
Determining the Original Amount
Before a Percent Change Example
• Metro Motors sold 112 cars this month. If this is
40% better than last month, how many cars
were sold last month?
Portion  112
Rate  100%  40%  140%  1.4
P
112
B 

 80 cars
R
1.4
© 2009 Cengage Learning. All rights reserved.
6–29
Determining the Original Amount Before
a Percent Change Example (cont’d)
• The second shift of a factory produced 17,010
units. If this amount was 5 ½% less than the
first shift, how many units were produced on the
first shift?
Portion  17,010
Rate  100%  5
1
2
%  94 12 0%  .945
P
17,010
B 

 18,000 units
R
.945
© 2009 Cengage Learning. All rights reserved.
6–30
Problems Involving Percentage Points
• percentage points
 A way of expressing a change from an original
amount to a new amount, without using a percent
sign.
Change in percentage points
Rate of
=
change
Original amount of percentage points
© 2009 Cengage Learning. All rights reserved.
6–31
Problems Involving Percentage Points
• After a vigorous promotion campaign, HiLo Mart
increased its market share from 5.4% to 8.1%, a
rise of 2.7 percentage points. What percent
increase in sales does this represent?
Portion  Increase  2.7%  .027
Base  5.4%  .054
P
.027
Rate of change 

 .5  50%
B
.054
© 2009 Cengage Learning. All rights reserved.
6–32
Problems Involving Percentage Points
• The unemployment rate in Glen Haven dropped
from 8.8% to 6.8% in the past year, a decrease
of 2 percentage points. What percent decrease
does this represent?
Portion  Decrease  2.0%  .020
Base  8.8%  .088
P .020
Rate of change  
 .2273  22.73%
B .088
© 2009 Cengage Learning. All rights reserved.
6–33
Chapter Review Problem 1
• Solve the following by converting to a decimal:
27%
.27
.81%
.0081
12 34 %
12.75%  .1275
23
5
%
© 2009 Cengage Learning. All rights reserved.
4 53 %  4.6%  .0046
6–34
Chapter Review Problem 2
• An ad read, “This week only, all merchandise
35% off!” If a television set normally sells for
$349.95, what is the amount of the savings?
Rate  35%
Base  Original Amount  349.95
P  R  B  .35  349.95  122.48
© 2009 Cengage Learning. All rights reserved.
6–35
Chapter Review Problem 3
• If 453 runners out of 620 completed a marathon,
what percent of the runners finished the race?
Portion  453
Base  Original Amount  620
P
453
R 

 .731  73.1%
B
620
© 2009 Cengage Learning. All rights reserved.
6–36
Chapter Review Problem 4
• By what percent is a 100-watt light bulb brighter
than a 60-watt bulb?
Portion  Increase  100  60  40
Base  Original Amount  60
P
40
R 

 .667  66.7%
B
60
© 2009 Cengage Learning. All rights reserved.
6–37
Chapter Review Problem 5
• A pre-election survey shows that the popularity
of a presidential candidate has increased from
26.5 percent to 31.3 percent of the electorate,
an increase of 4.8 percentage points. What
percent increase does this represent?
Portion  Increase  31.3  26.5  4.8
Base  Original Amount  26.5
P
4.8
R 

 .181  18.1%
B
26.5
© 2009 Cengage Learning. All rights reserved.
6–38