2. 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
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3. 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.
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4. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
10.8
Applications and Problem Solving with Inequalities a
Translate number sentences to inequalities.
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Slide 4

5. 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.
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6. 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.
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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
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
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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
1. Familiarize. Let n = the number of people in attendance.
2. Translate.
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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
3. Solve.
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10. 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 $ 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.
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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
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
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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
Familiarize. Let x = the number of grams of fat that
Anthony consumes on the fourth day.
2. Translate.
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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
3. Solve.
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14. 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.
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