OBJECTIVES

1.5 Applications and Problem Solving with Inequalities

dUse < or > for to

write a true statement in a situation like 6 10.

Slide 1Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

a Translate number sentences to inequalities.

b Solve applied problems using inequalities.

1.5 Applications and Problem Solving with Inequalities

a Translate number sentences to inequalities.

Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1.5 Applications and Problem Solving with Inequalities

a Translate number sentences to inequalities.

Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1.5 Applications and Problem Solving with Inequalities

aTranslate number sentences to inequalities.

TRANSLATING “AT LEAST” AND “AT MOST”

Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

1.5 Applications and Problem Solving with Inequalities

b Solve applied problems using inequalities.

Catering Costs

Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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

EXAMPLE

1.5 Applications and Problem Solving with Inequalities

b Solve applied problems using inequalities.

Catering Costs

Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1. Familiarize. Let n = the number of people in attendance.

2. Translate.

EXAMPLE

1.5 Applications and Problem Solving with Inequalities

b Solve applied problems using inequalities.

Catering Costs

Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

3. Solve.

EXAMPLE

1.5 Applications and Problem Solving with Inequalities

b Solve applied problems using inequalities.

Catering Costs

Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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.

EXAMPLE

1.5 Applications and Problem Solving with Inequalities

b Solve applied problems using inequalities.

Nutrition

Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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

EXAMPLE

1.5 Applications and Problem Solving with Inequalities

b Solve applied problems using inequalities.

Nutrition

Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

1. Familiarize. Let x = the number of grams of fat that Anthony consumes on the fourth day.

2. Translate.

EXAMPLE

1.5 Applications and Problem Solving with Inequalities

b Solve applied problems using inequalities.

Nutrition

Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

3. Solve.

EXAMPLE

1.5 Applications and Problem Solving with Inequalities

b Solve applied problems using inequalities.

Nutrition

Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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.