The Art of Problem Solving Chapter 1 The Art of Problem Solving 2012 Pearson Education, Inc.

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 2012 Pearson Education, Inc.

Calculating, Estimating, and Reading Graphs Section 1-4 Calculating, Estimating, and Reading Graphs 2012 Pearson Education, Inc.

Calculating, Estimating, and Reading Graphs Calculation Estimation Interpretation of Graphs 2012 Pearson Education, Inc.

Calculation There are many types of calculators such as four-function, 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. 2012 Pearson Education, Inc.

Calculation Below are some screen shots from a graphing calculator. 2012 Pearson Education, Inc.

Example: Calculation Solution Use your calculator to find the following: a) b) c) Solution a) 3.14159265 (approximately) b) 51 c) 5.0625 2012 Pearson Education, Inc.

Estimation There are many times when we only need an estimate to a problem and a calculator is not necessary. 2012 Pearson Education, Inc.

Example: Estimation Solution 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. 2012 Pearson Education, Inc.

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. 2012 Pearson Education, Inc.

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 F 10% D 10% A 15% B 25% C 40% 2012 Pearson Education, Inc.

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. 2012 Pearson Education, Inc.

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) 2001 2002 2003 2004 2005 a) Estimate the number of cups in 2004 What year shows the greatest decrease in cups? 2012 Pearson Education, Inc.

Bar Graph (Continued) Solution a) The number of cups in 2004 appears to be about 700. The year 2005 looks to have the greatest decrease at about 250 cups. 2012 Pearson Education, Inc.

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 ’01 ’02 ’03 ’04 ’05 In which years did the average class size increase from the previous year? How much did the average size increase from 2001 to 2003? 2012 Pearson Education, Inc.

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. 2012 Pearson Education, Inc.