Chapter 3

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Contemporary Business Mathematics
with Canadian Applications
Eighth Edition
S. A. Hummelbrunner/K. Suzanne Coombs
PowerPoint: D. Johnston
Chapter 3
Ratio, Proportion, and Percent
Copyright © 2008 Pearson Education Canada
3-1
Objectives
After completing chapter three, the student
will be able to:
• Set up ratios and solve allocation problems.
• Set up proportions and use proportions to
solve problems involving equivalence of
ratios.
• Find percents, rates percent, and the base
for problems involving percentages.
(continued)
Copyright © 2008 Pearson Education Canada
3-2
Objectives
(continued)
• Solve problems involving the percent of
increase and decrease.
• Solve business problems involving percents.
• Perform currency conversions.
• Set up an index number .
(continued)
Copyright © 2008 Pearson Education Canada
3-3
Objectives
(continued)
• Use the Consumer Price Index to determine
the purchasing power of the dollar and
compute real income.
• Compute federal income taxes using federal
income tax brackets and tax rates.
• Calculate simple rates of return between
two dates for mutual funds.
Copyright © 2008 Pearson Education Canada
3-4
Ratios
A ratio can be used to compare values.
Word
6 to 2
Colon
6:2
Fraction
6/2
Percent
300%
Decimal
3.0
Copyright © 2008 Pearson Education Canada
3-5
Allocation Involving Ratios
Allocate 660 in the Ratio of 3 : 2
Method A
Total number of parts is 3 + 2 = 5
Value of each part is
6605 = 132
3 x 132 = 396
2 x 132 = 264
Copyright © 2008 Pearson Education Canada
3-6
Allocation According to Ratios
•
•
•
•
•
Allocate 660 in the ratio of 3:2
Method B
3+2=5
(3/5) x 660 = 396
(2/5) x 660 = 264
Copyright © 2008 Pearson Education Canada
3-7
Proportions
A ratio can be expressed as the equality of two
fractions.
a: b = c: d
a c

b d
An important property of a proportion is that :
ad = bc
Copyright © 2008 Pearson Education Canada
3-8
Basic Percentage Problem
Percentage = Rate x Base
40 % of 50 = 0.4 x 50 = 20
Rate
40 %
Base (original value)
50
Percentage
(new value)
20
Copyright © 2008 Pearson Education Canada
3-9
Finding the Rate
Rate = Percentage = New Number
Base
Original Number
$50 is what percent of $800
Rate = 50 = 6.25%
800
Copyright © 2008 Pearson Education Canada
3-10
Finding the Base
Base = Percentage
Rate
$36 is 6% of what number?
Base = $36 = $600
.06
Copyright © 2008 Pearson Education Canada
3-11
Finding Rate of Increase or
Decrease
Rate of change = Amount of Change
Original Number
$325 is what percent more than $200?
Solution: (325-200) = 62.5% increase
200
What percent less than $200 is $180?
Solution: (180-200) = -10%
200
decrease
Copyright © 2008 Pearson Education Canada
3-12
Currency Conversion
The exchange rate equals the value of
one nation’s currency expressed in
terms of another nation’s currency.
Copyright © 2008 Pearson Education Canada
3-13
Exchange Rates
Canadian Dollars
U.S Dollars
1.39
1.00
U.S. Dollars
Canadian Dollars
1.00 = 0.72
1.39
Convert $100
Canadian to U.S.
$100 x 0.72 = $72
Copyright © 2008 Pearson Education Canada
3-14
Index Numbers
• An index number expresses the relative
change in the value of an item at different
points in time.
Copyright © 2008 Pearson Education Canada
3-15
Index Numbers
Price of text in 2004
$112.00
Price of text in 2000
$ 90.00
Price of text in 2004
Price of text in 2000
112 = 1.244 = 1.244%
90
Base period
Index number
Year 2000
1.244 (an increase of
24.4% in the price)
Copyright © 2008 Pearson Education Canada
3-16
Consumer Price Index
• Most widely used indicator of changes in
overall level of goods and services in
Canada
• Currently based on 1992 price levels
• Published monthly by Statistics Canada
Copyright © 2008 Pearson Education Canada
3-17
Purchasing Power of Dollar
The purchasing power of the dollar is the
reciprocal of the Consumer Price Index (CPI).
Purchasing Power of Dollar = $1
CPI
Real Income =Income in Current Dollars(100)
Consumer Price Index
Copyright © 2008 Pearson Education Canada
3-18
Calculating Real Income
John earned $42,000 on 2002. Calculate his
real income in terms of 1992 dollars. The
base year is 1992, and the CPI for 2002 was
120.4 .
Real income or purchasing power =
42,000 (100) = 34, 883.72
120.4
Copyright © 2008 Pearson Education Canada
3-19
Personal Income Taxes
• Taxes imposed by the federal and provincial
governments on the earned income of
residents of Canada.
• Income tax brackets for 2006 are shown in
Table 3.3 in your text.
• The brackets are adjusted annually based on
changes in the CPI in excess of 3%
Copyright © 2008 Pearson Education Canada
3-20
Marginal Tax Rate
• The rate at which your next dollar of earned
income is taxed.
• Directly proportional to your earnings and
the tax bracket you are in.
• Varies from province to province depending
on tax rates and surtaxes in the particular
provinces.
Copyright © 2008 Pearson Education Canada
3-21
Summary
• Ratios, proportions, and percents are tools
used in applications dealing with percent
increase or decrease, currency conversion,
index numbers, and personal income taxes.
Copyright © 2008 Pearson Education Canada
3-22

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