Chapter 1
The Art of
Problem
Solving
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Chapter 1: The Art of Problem Solving
1.1 Solving Problems by Inductive
Reasoning
1.2 An Application of Inductive Reasoning:
Number Patterns
1.3 Strategies for Problem Solving
1.4 Calculating, Estimating, and Reading
Graphs
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Chapter 1
Section 1-4
Calculating, Estimating, and
Reading Graphs
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Calculating, Estimating, and Reading
Graphs
• Calculation
• Estimation
• Interpretation of Graphs
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Calculation
There are many types of calculators such as fourfunction, scientific, and graphing.
There are also many different models available and
you may need to refer to your owner’s manual for
assistance. Other resources for help are instructors
and students that have experience with that model.
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Calculation
Below are some screen shots from a graphing
calculator.
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Example: Calculation
Use your calculator to find the following:
a) 
b) 2601
4
c) 1.5
Solution
a) 3.14159265 (approximately)
b) 51
c) 5.0625
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Estimation
There are many times when we only need an
estimate to a problem and a calculator is not
necessary.
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Example: Estimation
A 20-ounce box of cereal sells for $3.12.
Approximate the cost per ounce.
Solution
Because it is an approximation, we can say
that the cost is about $3.00 for 20 ounces.
This works out to 3.00/20 = $0.15 per
ounce.
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Interpretation of Graphs
Using graphs is an efficient way to transmit
information. Some of the common types of
graphs are circle graphs (pie charts), bar
graphs, and line graphs.
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Example: Circle Graph (Pie Chart)
Use the circle graph below to determine how
many of the 140 students made an A or a B.
Letter Grades in College Algebra
D
10%
F
10%
C
40%
A
15%
B
25%
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Circle Graph (Continued)
Solution
Notice that there were 15% A’s and 25% B’s.
For 140 students this yields:
A: 0.15 x 140 = 21
B: 0.25 x 140 = 35
which is a total of 56 students.
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Example: Bar Graph
The bar graph shows the number of cups of coffee, in
hundreds of cups, that a professor had in a given year.
Cups
(in hundreds)
10
8
6
4
2
0
2001 2002 2003 2004 2005
a) Estimate the number of cups in 2004
b) What year shows the greatest decrease in cups?
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Bar Graph (Continued)
Solution
a) The number of cups in 2004 appears to be
about 700.
b) The year 2005 looks to have the greatest
decrease at about 250 cups.
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Example: Line Graph
The line graph shows the average class size of a first grade
class at a grade school for years 2001 though 2005.
Students per
class
34
30
26
22
18
14
’01 ’02
’03
’04
’05
a)
In which years did the average class size increase
from the previous year?
b) How much did the average size increase from 2001
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to 2003?
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Line Graph (Continued)
Solution
a) The average class size increased in years
2002, 2003, and 2004.
b) The average class size was 16 in 2001 and
28 in 2003 which would indicate an
increase of 12 students per class.
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