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

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities a Translate number sentences to inequalities. b Solve applied problems using inequalities. d Use < or > for  to write a true statement in a situation like 6  10. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 3

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities a Translate number sentences to inequalities. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 4

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities a Translate number sentences to inequalities. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 5

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities TRANSLATING “AT LEAST” AND “AT MOST” a Translate number sentences to inequalities. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 6

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities b Solve applied problems using inequalities. 1 Catering Costs To cater a party, Curtis’ Barbeque charges a $150 setup fee plus $15.50 per person. The cost of Berry Manufacturing’s annual picnic cannot exceed $2100. How many people can attend the picnic? Source: Curtis’ All American Barbeque, Putney, Vermont Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 7

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities b Solve applied problems using inequalities. 1 Catering Costs 1. Familiarize. Let n = the number of people in attendance. 2. Translate. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 8

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities b Solve applied problems using inequalities. 1 Catering Costs 3. Solve. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 9

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities b Solve applied problems using inequalities. 1 Catering Costs 4. Check. Although the solution set of the inequality is all numbers less than or equal to about 125.8, since n = the number of people in attendance, we round down to 125 people. If 125 people attend, the cost will be $150 + $15.50(125), or $2087.50. If 126 attend, the cost will exceed $2100. 5. State. At most, 125 people can attend the picnic. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 10

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities b Solve applied problems using inequalities. 2 Nutrition The U.S. Department of Agriculture recommends that for a typical 2000-calorie daily diet, no more than 20 g of saturated fat be consumed. In the first three days of a four-day vacation, Anthony consumed 26 g, 17 g, and 22 g of saturated fat. Determine (in terms of an inequality) how many grams of saturated fat Anthony can consume on the fourth day if he is to average no more than 20 g of saturated fat per day. SOURCES: U.S. Department of Health and Human Services; U.S. Department of Agriculture Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 11

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities b Solve applied problems using inequalities. 2 Nutrition Familiarize. Let x = the number of grams of fat that Anthony consumes on the fourth day. 2. Translate. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 12

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities b Solve applied problems using inequalities. 2 Nutrition 3. Solve. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 13

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 10.8 Applications and Problem Solving with Inequalities b Solve applied problems using inequalities. 2 Nutrition 4. Check. As a partial check, we show that Anthony can consume 15 g of saturated fat on the fourth day and not exceed a 20-g average for the four days: 5. State. Anthony’s average intake of saturated fat for the vacation will not exceed 20 g per day if he consumes no more than 15 g of saturated fat on the fourth day. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 14