2. CHAPTER 1 Whole Numbers Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1.1Standard Notation 1.2Addition 1.3Subtraction 1.4Multiplication 1.5Division 1.6Rounding and Estimating; Order 1.7Solving Equations 1.8Applications and Problem Solving 1.9Exponential Notation and Order of Operations

3. OBJECTIVES 1.8 Applications and Problem Solving Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aSolve applied problems involving addition, subtraction, multiplication, or division of whole numbers.

4. 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. One of the most important ways in which we use mathematics is as a tool in solving problems. To solve a problem, we use the five-step strategy. The first of these five steps, becoming familiar with the problem, is probably the most important. It provides a solid foundation for translating the problem to an equation that represents the situation accurately.

5. 1.8 Applications and Problem Solving FIVE STEPS FOR PROBLEM SOLVING Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize yourself with the problem situation. If the problem is presented in words, this means to read and reread it carefully until you understand what you are being asked to find. Some or all of the following can also be helpful. a) Make a drawing, if it makes sense to do so. b) Make a written list of the known facts and a list of what you wish to find out. c) Assign a letter, or variable, to the unknown.

6. 1.8 Applications and Problem Solving FIVE STEPS FOR PROBLEM SOLVING Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. d) Organize the information in a chart or a table. e) Find further information. Look up a formula, consult a reference book or an expert in the field, or do research on the Internet. f) Guess or estimate the answer and check your guess or estimate. 2. Translate the problem to an equation using the variable. 3. Solve the equation.

7. 1.8 Applications and Problem Solving FIVE STEPS FOR PROBLEM SOLVING Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check to see whether your possible solution actually fits the problem situation and is thus really a solution of the problem. Although you may have solved an equation, the solution of the equation might not be a solution of the original problem. 5. State the answer clearly using a complete sentence and appropriate units.

8. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 2Checking Account Balance. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The balance in Francisco’s checking account is $573. He uses his debit card to buy a juicer that costs $99. Find the new balance in his checking account.

9. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 2Checking Account Balance. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We first make a drawing or at least visualize the situation. We let B = the new balance in Francisco’s checking account. We start with $573 and take away $99.

10. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 2Checking Account Balance. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate. We translate to an equation:

11. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 2Checking Account Balance. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve. This equation tells us what to do. We subtract.

12. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 2Checking Account Balance. Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. To check our answer of $474, we can repeat the calculation. We can also note that the answer should be less than the original amount, $573, and it is. Another way to check is to add the money spent, $99, to the new balance, $474: $99 + $474 = $573. We get the original balance, so the answer checks. We can also estimate: This tells us that the answer is reasonable.

13. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 2Checking Account Balance. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 5. State. The new balance in Francisco’s checking account is $474.

14. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 4Total Cost of Chairs. Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We let C = the cost of 6 chairs. What is the total cost of 6 Adirondack chairs if each one costs $169?

15. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 4Total Cost of Chairs. Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate. 3. Solve.

16. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 4Total Cost of Chairs. Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. 5. State. The total cost of 6 chairs is $1014. The answer checks.

17. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 7Automobile Mileage. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The 2009 Toyota Matrix gets 21 miles to the gallon (mpg) in city driving. How many gallons will it use in 3843 mi of city driving? Source: Toyota 1. Familiarize. We let g = the number of gallons of gasoline used in 3843 mi of city driving.

18. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 7Automobile Mileage. Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate.

19. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 7Automobile Mileage. Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve.

20. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 7Automobile Mileage. Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. 5. State. The Toyota Matrix will use 183 gal of gasoline. The answer checks.

21. 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Sometimes we must use more than one operation to solve a problem.

22. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 8Weight Loss. Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To lose one pound, you must burn about 3500 calories in excess of the calories you consume. The chart on the next slide shows how long a person must engage in several types of exercise in order to burn 100 calories. For how long would a person have to run at a brisk pace in order to lose one pound?

23. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 8Weight Loss. Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

24. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 8Weight Loss. Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Familiarize. We will first find how many hundreds are in 3500. This will tell us how many times a person must run for 8 min in order to lose one pound. Then we will multiply to find the total number of minutes required for the weight loss. We let x = the number of hundreds in 3500.

25. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 8Weight Loss. Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 2. Translate.

26. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 8Weight Loss. Slide 26Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Solve.

27. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 8Weight Loss. Slide 27Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We know that running for 8 min will burn 100 calories. This must be done 35 times in order to lose one pound. We let t = the time it takes to lose one pound. Thus we have the following.

28. EXAMPLE 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. 8Weight Loss. Slide 28Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 4. Check. 5. State. You must run for 280 min, or 4 hr 40 min, at a brisk pace in order to lose one pound. The answer checks.

29. 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. Slide 29Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

30. 1.8 Applications and Problem Solving a Solve applied problems involving addition, subtraction, multiplication, or division of whole numbers. Slide 30Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

31. Title 1.8 Applications and Problem Solving Slide 31Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 1. Look for patterns when solving problems. Each time you study an example in the text, you may observe a pattern for problems found later in the exercise sets or in other practical situations. 2. When translating in mathematics, consider the dimensions of the variables and constants in the equation. The variables that represent length should all be in the same unit, those that represent money should all be in dollars or all in cents, and so on.

32. Title 1.8 Applications and Problem Solving Slide 32Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 3. Make sure that units appear in the answer whenever appropriate and that you completely answer the original problem.