Percents and Their Applications in Business CHAPTER 6 Percents and Their Applications in Business © 2009 Cengage Learning. All rights reserved.

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.

Understanding Equations Formula A mathematical representation of a fact, rule, principle, or other logical relation in which letters represent number quantities. Equation A mathematical statement expressing a relationship of equality; usually written as a series of symbols that are separated into left and right sides and joined by an equal sign. X + 7 = 10 is an equation. Expression A mathematical operation or a quantity stated in symbolic form, not containing an equal sign. X + 7 is an expression. Constants (Knowns) The parts of an equation that are given. In equations, the knowns are constants (numbers), which are quantities having a fixed value. In the equation X + 7 = 10, 7 and 10 are the knowns or constants. Terms The knowns (constants) and unknowns (variables) of an equation. In the equation X + 7 = 10, the terms are X, 7, and 10. Solve an Equation The process of finding the numerical value of the unknown in an equation. © 2009 Cengage Learning. All rights reserved.

Understanding and Converting Percents 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.

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

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

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

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

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

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

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

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

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

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.

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

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

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.

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.

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.

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.

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.

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.

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

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.

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.

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

Determining the New Amount After a 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.

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

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.

Determining the Original Amount Before a 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.

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

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.

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.

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

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.

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.

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.

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.