CHAPTER 10 Solving Equations and Inequalities Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.1Solving Equations: The Addition Principle 10.2Solving Equations: The Multiplication Principle 10.3Using the Principles Together 10.4Formulas 10.5Applications of Percent 10.6Applications and Problem Solving 10.7Solving Inequalities 10.8Applications and Problem Solving with Inequalities

OBJECTIVES 10.5 Applications of Percent Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aSolve applied problems involving percent.

10.5 Applications of Percent a Solve applied problems involving percent. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. In solving percent problems, we first translate the problem to an equation. Then we solve the equation.

10.5 Applications of Percent KEY WORDS IN PERCENT TRANSLATIONS Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 1 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 2 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 3 Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

10.5 Applications of Percent a Solve applied problems involving percent. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Percent problems are actually of three different types.

10.5 Applications of Percent Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

10.5 Applications of Percent a Solve applied problems involving percent. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Each of the three types of percent problem depends on which of the three pieces of information is missing in the statement

10.5 Applications of Percent a Solve applied problems involving percent. Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 4 Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Solve: The letter is by itself. To solve the equation, we need only convert 11% to decimal notation and multiply: Thus, 5.39 is 11% of 49. The answer is 5.39.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 5 Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3 is 16% of what number?

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 5 Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 6 Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 6 Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 7Foreign Visitors to China Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. About 22 million foreign travelers visited China in Of this number, 9% were from the United States. How many Americans visited China in 2006? Source: TIME Magazine, March 8, 2007

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 7Foreign Visitors to China Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To solve this problem, we first reword and then translate. We let a = the number of Americans, in millions, who visited China in 2006.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 7 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Solve: The letter is by itself. To solve the equation, we need only convert 9% to decimal notation and multiply: Thus, 1.98 million is 9% of 22 million, so 1.98 million Americans visited China in 2006.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 8Public School Enrollment Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. In the fall of 2008, 14.9 million students enrolled in grades 9–12 in U.S. public schools. This was 30% of the total enrollment in public schools. What was the total enrollment? Source: National Center for Educational Statistics

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 8Public School Enrollment Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To solve this problem, we first reword and then translate. We let t = the total enrollment, in millions, in U.S. public schools in 2008.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 8Public School Enrollment Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Solve: To solve the equation, we convert 30% to decimal notation and divide by 0.3 on both sides: About 49.7 million students enrolled in U.S. public schools in 2008.

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 9Employment Outlook Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. There were 280 thousand dental assistants in This number is expected to grow to 362 thousand in What is the percent of increase? Source: Occupational Outlook Handbook

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 9Employment Outlook Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To solve the problem, we must first determine the amount of the increase, in thousands:

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 9Employment Outlook Slide 26Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Using the job increase of 82 thousand, we reword and then translate. We let p = the percent of increase. We want to know, “what percent of the number of jobs in 2006 is 82 thousand?”

EXAMPLE 10.5 Applications of Percent a Solve applied problems involving percent. 9Employment Outlook Slide 27Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Solve: To solve the equation, we divide by 280 on both sides and convert the answer to percent notation: The percent of increase is about 29.3 %.