Percents and Their Applications in Business

1. CHAPTER 6 Percents and Their Applicationsin Business © 2009 Cengage Learning. All rights reserved.

2. PERFORMANCE OBJECTIVES Section I Understanding and Converting Percents 6-1: Converting percents to decimals and decimals to percents 6-2: Converting percents to fractions and fractions to percents Section II Using the Percentage Formula to Solve Business Problems 6-3: Solving for the portion 6-4: Solving for the rate 6-5: Solving for the base Section III Solving Other Business Problems Involving Percents 6-6: Determining rate of increase or decrease 6-7: Determining amounts in increase or decrease situations 6-8: Understanding and solving problems involving percentage points © 2009 Cengage Learning. All rights reserved.

3. Understanding Equations © 2009 Cengage Learning. All rights reserved.

4. Understanding and Converting Percents • percent • A way of representing the parts of a whole. Percent means per hundred or parts per hundred. • percent sign • The symbol, %, used to represent percents. For example, 1 percent would be written 1%. © 2009 Cengage Learning. All rights reserved.

5. Converting Percents to Decimals © 2009 Cengage Learning. All rights reserved.

6. Converting Percents to Decimals Example 28% .28 13.4% .134 6½% = 6.5% .065 .02% .0002 © 2009 Cengage Learning. All rights reserved.

7. Converting Decimals to Percents © 2009 Cengage Learning. All rights reserved.

8. Converting Decimals to Percents Example 3.5 350% .345 = 34.5% .34½ .00935 .935% 5.33 533% © 2009 Cengage Learning. All rights reserved.

9. Converting Percents to Fractions © 2009 Cengage Learning. All rights reserved.

10. Converting Percents to Fractions Example © 2009 Cengage Learning. All rights reserved.

11. Converting Percents to Fractions Example (cont’d) © 2009 Cengage Learning. All rights reserved.

12. Converting Fractions to Percents © 2009 Cengage Learning. All rights reserved.

13. Converting Fractions to Percents © 2009 Cengage Learning. All rights reserved.

14. Using the Percentage Formula to Solve Business Problems • base • The variable of the percentage formula that represents 100%, or the whole thing. • portion • The variable of the percentage formula that represents a part of the base. • rate • The variable of the percentage formula that defines how much or what part the portion is of the base. The rate is the variable with the percent sign. © 2009 Cengage Learning. All rights reserved.

15. Steps for Solving Percentage Problems © 2009 Cengage Learning. All rights reserved.

16. The Magic Triangle © 2009 Cengage Learning. All rights reserved.

17. Sample Percentage Problems • Maritza Torres owns 37% of a travel agency. • If the total worth of the business is $160,000, how much is Maritza’s share? © 2009 Cengage Learning. All rights reserved.

18. Sample Percentage Problems (cont’d) • What is the sales tax in a state where the tax on a purchase of $464 is $25.52? © 2009 Cengage Learning. All rights reserved.

19. Sample Percentage Problems (cont’d) • The Daily Times reports that 28% of its advertising is for department stores. • If the department store advertising amounts to $46,200, what is the total advertising revenue of the newspaper? © 2009 Cengage Learning. All rights reserved.

20. Sample Percentage Problems (cont’d) • Lisa Walden, a sales associate for a large company, successfully makes the sale on 40% of her sales presentations. • If she made 25 presentations last week, how many sales did she make? © 2009 Cengage Learning. All rights reserved.

21. Sample Percentage Problems (cont’d) • A quality control process finds 17.2 defects for every 8,600 units of production. • What percent of the production is defective? © 2009 Cengage Learning. All rights reserved.

22. Sample Percentage Problems (cont’d) • The Bentley Bobcats have won 80% of their basketball games. If they lost 4 games, how many games have been played? Won = 80% Lost = 20% © 2009 Cengage Learning. All rights reserved.

23. Determining Rate of Increase or Decrease © 2009 Cengage Learning. All rights reserved.

24. Rate of Increase or Decrease Example • Allied Plumbing sold 2,390 feet of 5/8-inch galvanized pipe in July. If 2,558 feet were sold in August, what is the percent increase in pipe footage sales? © 2009 Cengage Learning. All rights reserved.

25. Rate of Increase or Decrease Example • The supermarket price of yellow onions dropped from $.59 per pound to $.45 per pound. What is the percent decrease in the price of onions? © 2009 Cengage Learning. All rights reserved.

26. Determining the New Amount After a Percent Change © 2009 Cengage Learning. All rights reserved.

27. Determining the New Amount Aftera Percent Change Example • Economists predict that next year housing prices will drop by 4%. This year’s price for an average house is $110,000. What will the average price of a house be next year? © 2009 Cengage Learning. All rights reserved.

28. Determining the Original Amount Before a Percent Change © 2009 Cengage Learning. All rights reserved.

29. Determining the Original Amount Before a Percent Change Example • Metro Motors sold 112 cars this month. If this is 40% better than last month, how many cars were sold last month? © 2009 Cengage Learning. All rights reserved.

30. Determining the Original Amount Beforea Percent Change Example (cont’d) • The second shift of a factory produced 17,010 units. If this amount was 5 ½% less than the first shift, how many units were produced on the first shift? © 2009 Cengage Learning. All rights reserved.

31. Problems Involving Percentage Points • percentage points • A way of expressing a change from an original amount to a new amount, without using a percent sign. © 2009 Cengage Learning. All rights reserved.

32. Problems Involving Percentage Points • After a vigorous promotion campaign, HiLo Mart increased its market share from 5.4% to 8.1%, a rise of 2.7 percentage points. What percent increase in sales does this represent? © 2009 Cengage Learning. All rights reserved.

33. Problems Involving Percentage Points • The unemployment rate in Glen Haven dropped from 8.8% to 6.8% in the past year, a decrease of 2 percentage points. What percent decrease does this represent? © 2009 Cengage Learning. All rights reserved.

34. Chapter Review Problem 1 • Solve the following by converting to a decimal: © 2009 Cengage Learning. All rights reserved.

35. Chapter Review Problem 2 • An ad read, “This week only, all merchandise 35% off!” If a television set normally sells for $349.95, what is the amount of the savings? © 2009 Cengage Learning. All rights reserved.

36. Chapter Review Problem 3 • If 453 runners out of 620 completed a marathon, what percent of the runners finished the race? © 2009 Cengage Learning. All rights reserved.

37. Chapter Review Problem 4 • By what percent is a 100-watt light bulb brighter than a 60-watt bulb? © 2009 Cengage Learning. All rights reserved.

38. Chapter Review Problem 5 • A pre-election survey shows that the popularity of a presidential candidate has increased from 26.5 percent to 31.3 percent of the electorate, an increase of 4.8 percentage points. What percent increase does this represent? © 2009 Cengage Learning. All rights reserved.