1. 1 Alan S. Tussy R. David Gustafson Prealgebra Second Edition Copyright © 2002 Wadsworth Group.

2. 2 3.1 Variables and Algebraic Expressions In this section, you will learn about Algebraic expressions Translating from English to mathematical symbols Writing algebraic expressions to represent unknown quantities Looking for hidden operations Expressions involving more than one operation

3. 3 Algebraic expressions

4. 4 Translating from English to mathematical symbols

5. 5

6. 6

7. 7

8. 8 Writing algebraic expressions to represent unknown quantities Self Check A van weighs p pounds. A car is 1,000 pounds lighter than the van. How many pounds does the car weigh?

9. 9 EXAMPLE 3 Writing an algebraic expression. The pipe in Figure 3-1 is k feet in length. It is to be cut into 5 equally long pieces. How long will each piece be?

10. 10 EXAMPLE 4 Naming two unknown quantities. In Figure 3-2, the baseball card’s value is 4 times that of the football card. Choose a variable to represent the value of one card. Then write an expression for the value of the other card.

11. 11 EXAMPLE 5 Naming two unknown quantities. A 72-inch-long sub sandwich is cut into two pieces. Choose a variable to represent the length of one piece. Then write an expression for the length of the other piece.

12. 12 EXAMPLE 6 Hidden operations. The Golden Gate Bridge was completed 28 years before the Houston Astrodome was opened. The World Trade Center in New York was built 8 years after the Astrodome. Use algebraic expressions to express the ages (in years) of each of these engineering wonders.

13. 13 EXAMPLE 7 Looking for a pattern. How many eggs are there in d dozen?

14. 14 Expressions involving more than one operation EXAMPLE 8 An expression involving two operations. As Figure 3-3 shows, Alaska is much larger than Vermont. To be exact, the area of Alaska is 380 square miles more than 50 times that of Vermont. Choose a variable to represent one area. Then write an expression for the other area.

15. 15 3.2 Evaluating Algebraic Expressions and Formulas In this section, you will learn about Evaluating algebraic expressions Formulas Formulas from business Formulas from science Formulas from mathematics

16. 16 Evaluating algebraic expressions The manufacturer’s instructions for installing a kitchen garbage disposal include the diagram in Figure 3-4. Word phrases are used to describe the lengths of the pieces of pipe needed to connect the disposal to the drain line.

17. 17 Formulas from business

18. 18 Formulas from business

19. 19 Formulas from business

20. 20 Formulas from science

21. 21 EXAMPLE 4 Highway speed limits. Several state speed limits for trucks are shown below. At each of these speeds, how far would a truck travel in 3 hours?

22. 22 Degrees Fahrenheit to Degrees Celsius Electronic message boards in front of some banks flash two temperature readings. This is because temperature can be measured using the Fahrenheit or the Celsius scale. The Fahrenheit scale is used in the American system of measurement and the Celsius scale in the metric system. The two scales are shown on the thermometers in Figure 3-6. This should help you to see how the two scales are related. There is a formula to convert a Fahrenheit reading F to a Celsius reading C:

23. 23 Formulas from science

24. 24 Formulas from mathematics

25. 25 EXAMPLE 7 Response time to 911 calls. To measure its effectiveness, a police department recorded the length of time between incoming 911 calls and the arrival of a police unit at the scene. The response times for an entire week are listed in Table 3-2. Find the average response time.

26. 26 3.3 Simplifying Algebraic Expressions and the Distributive Property In this section, you will learn about Simplifying algebraic expressions involving multiplication The distributive property Distributing a factor of - 1 Extending the distributive property

27. 27 The distributive property

28. 28 The distributive property

29. 29 The distributive property

30. 30 Distributing a factor of 1

31. 31 Extending the distributive property

32. 32 3.4 Combining Like Terms In this section, you will learn about Terms of an algebraic expression Coefficients of a term Terms and factors Like terms Combining like terms Perimeter formulas

33. 33 Terms of an algebraic expression

34. 34 Numerical Coefficient

35. 35 Coefficients of a term

36. 36 Terms and factors

37. 37 Like terms

38. 38 Combining like terms

39. 39 Combining like terms

40. 40 Combining like terms

41. 41 Perimeter formulas

42. 42 Perimeter formulas

43. 43 EXAMPLE 11 Energy conservation. See Figure 3-9. Find the cost to weatherstrip the front door and window of the house if the material costs 20¢ a foot.

44. 44 3.5 Simplifying Expressions to Solve Equations In this section, you will learn about Checking solutions Combining like terms to solve equations Variables on both sides of an equation Removing parentheses A strategy for solving equations

45. 45 Checking solutions

46. 46 Combining like terms to solve equations

47. 47 Variables on both sides of an equation

48. 48 Removing parentheses

49. 49 Strategy for solving equations

50. 50 3.6 Problem Solving In this section, you will learn about Problems involving one unknown quantity Problems involving two unknown quantities Number and value

51. 51 Problems involving one unknown quantity EXAMPLE 1 Volunteer service hours. To receive a degree in child development, students at one college must complete 135 hours of volunteer service by working 3-hour shifts at a local preschool. If a student has already volunteered 87 hours, how many more 3-hour shifts must she work to meet the service requirement for her degree?

52. 52 Problems involving one unknown quantity EXAMPLE 2 Attorney’s fees. In return for her services, an attorney and her client split the jury’s cash award evenly. After paying her assistant $1,000, the lawyer ended up making $10,000 from the case. What was the amount of the award?

53. 53 Problems involving two unknown quantities EXAMPLE 3 Civil service exam. A candidate for a position with the FBI scored 12 points higher on the written portion of the civil service exam than she did on her interview. If her combined score was 92, what was her score on the interview?

54. 54 Problems involving two unknown quantities EXAMPLE 4 Playground design. After receiving a donation of 400 feet of chain link fencing, the staff of a preschool decided to use it to enclose a playground. Find the width of the playground if it is to be rectangular in shape, with the length three times the width.

55. 55 Number and value Suppose Delicious apples sell for 89 cents a pound. Find the cost of a. 5 pounds of apples, b. p pounds of apples, and c. (p – 2) pounds of apples. EXAMPLE 5 Number and value.

56. 56 Number and value EXAMPLE 6 Number and value. Ninety-five people attended a movie matinee. Ticket prices were $6 for adults and $4 for children. Find the income received from the sale of children’s tickets and from the sale of adults’ tickets. Use a table to present your results.

57. 57 Number and value EXAMPLE 7 Basketball. On a night when they scored 110 points, a basketball team made only 5 free throws (worth 1 point each). The remainder of their points came from two- and three-point baskets. If the number of baskets from the field totaled 45, how many two-point and how many three-point baskets did they make?