5. applications and problem solving with inequalities
1. 1.5
Applications and Problem Solving
with Inequalities
OBJECTIVES
a Translate number sentences to inequalities.
b Solve applied problems using inequalities.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 1
2. 1.5
Applications and Problem Solving
with Inequalities
a Translate number sentences to inequalities.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 2
3. 1.5
Applications and Problem Solving
with Inequalities
a Translate number sentences to inequalities.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 3
4. 1.5
Applications and Problem Solving
with Inequalities
TRANSLATING “AT LEAST” AND “AT MOST”
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 4
5. 1.5
Applications and Problem Solving
with Inequalities
b Solve applied problems using inequalities.
EXAMPLE
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 5
6. 1.5
Applications and Problem Solving
with Inequalities
b Solve applied problems using inequalities.
EXAMPLE
Catering Costs
1. Familiarize. Let n = the number of people in attendance.
2. Translate.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 6
7. 1.5
Applications and Problem Solving
with Inequalities
b Solve applied problems using inequalities.
EXAMPLE
Catering Costs
3. Solve.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 7
8. 1.5
Applications and Problem Solving
with Inequalities
b Solve applied problems using inequalities.
EXAMPLE
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 8
9. 1.5
Applications and Problem Solving
with Inequalities
b Solve applied problems using inequalities.
EXAMPLE
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 9
10. 1.5
Applications and Problem Solving
with Inequalities
b Solve applied problems using inequalities.
EXAMPLE
Nutrition
1. 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 10
11. 1.5
Applications and Problem Solving
with Inequalities
b Solve applied problems using inequalities.
EXAMPLE
Nutrition
3. Solve.
Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Slide 11
12. 1.5
Applications and Problem Solving
with Inequalities
b Solve applied problems using inequalities.
EXAMPLE
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 12