PowerPoint Presentation by Charlie Cook The University of West Alabama © 2009 Cengage Learning. All rights reserved. Percents and Their Applications in.

© 2009 Cengage Learning. All rights reserved.© 2009 Cengage Learning. All rights reserved.

PowerPoint Presentation by Charlie CookThe University of West Alabama

PowerPoint Presentation by Charlie CookThe University of West Alabama

Percents and

Their Applications

in Business

Percents and

Their Applications

in Business

CHAPTER 6

© 2009 Cengage Learning. All rights reserved. 6–2

PERFORMANCE OBJECTIVESPERFORMANCE OBJECTIVESPERFORMANCE OBJECTIVESPERFORMANCE 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


Understanding EquationsUnderstanding 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.


Understanding and Converting Understanding and Converting PercentsPercents

• percentpercent A way of representing the parts of a whole. Percent A way of representing the parts of a whole. Percent

means per hundred or parts per hundred.means per hundred or parts per hundred.

• percent signpercent sign The symbol, %, used to represent percents. For The symbol, %, used to represent percents. For

example, 1 percent would be written 1%.example, 1 percent would be written 1%.


Converting Percents to DecimalsConverting Percents to Decimals


Converting Percents to Decimals Converting Percents to Decimals ExampleExample

28% .28

13.4% .134

.0656½% = 6.5%

.0002.02%


Converting Decimals to PercentsConverting Decimals to Percents


Converting Decimals to Percents Converting Decimals to Percents ExampleExample

3.5

.34½

350%

.345 = 34.5%

.935%

533%

.00935

5.33


Converting Percents to FractionsConverting Percents to Fractions


Converting Percents to Fractions Converting Percents to Fractions ExampleExample

201

1005

%5

83

20075

1001

275

1001

37%5.37 21

85

200125

1001

2125

1001

62%21

62 21

1251

10008

1001

108

%8.


Converting Percents to Fractions Converting Percents to Fractions Example (cont’d)Example (cont’d)

103

10030 22

100230

%230

21

10050 44

100450

%450

1251

10008

1001

108

%8.


Converting Fractions to PercentsConverting Fractions to Percents

%7575.43

%2404.22512

52

%12525.11100125

41


Converting Fractions to PercentsConverting Fractions to Percents

%7575.43

%2404.22512

52

%12525.11100125

41

%32525.332478

41

%4202.44 51


Using the Percentage Formula Using the Percentage Formula to Solve Business Problemsto Solve Business Problems

• basebase The variable of the percentage formula that The variable of the percentage formula that

represents 100%, or the whole thing.represents 100%, or the whole thing.

• portionportion The variable of the percentage formula that The variable of the percentage formula that

represents a part of the base.represents a part of the base.

• raterate The variable of the percentage formula that defines The variable of the percentage formula that defines

how much or what part the portion is of the base. The how much or what part the portion is of the base. The rate is the variable with the percent sign.rate is the variable with the percent sign.


Steps for Solving Percentage Steps for Solving Percentage ProblemsProblems


The Magic TriangleThe Magic Triangle


Sample Percentage ProblemsSample Percentage Problems

• Maritza Torres owns 37% of a travel agency.Maritza Torres owns 37% of a travel agency.• If the total worth of the business is $160,000, If the total worth of the business is $160,000,

how much is Maritza’s share?how much is Maritza’s share?

200,59000,16037.BRP


Sample Percentage Problems (cont’d)Sample Percentage Problems (cont’d)

• What is the sales tax in a state where the tax on What is the sales tax in a state where the tax on a purchase of $464 is $25.52?a purchase of $464 is $25.52?

%5.5055.464

52.25BP

R



• The Daily TimesThe Daily Times reports that 28% of its advertising is for reports that 28% of its advertising is for department stores. department stores.

• If the department store advertising amounts to $46,200, If the department store advertising amounts to $46,200, what is the total advertising revenue of the newspaper?what is the total advertising revenue of the newspaper?

000,16528.

220,46

R

PB



• Lisa Walden, a sales associate for a large company, Lisa Walden, a sales associate for a large company, successfully makes the sale on 40% of her sales successfully makes the sale on 40% of her sales presentations. presentations.

• If she made 25 presentations last week, how many sales If she made 25 presentations last week, how many sales did she make?did she make?

10254.BRP



• A quality control process finds 17.2 defects for A quality control process finds 17.2 defects for every 8,600 units of production. every 8,600 units of production.

• What percent of the production is defective?What percent of the production is defective?

%2.0002.600,82.17

BP

R



• The Bentley Bobcats have won 80% of their The Bentley Bobcats have won 80% of their basketball games. If they lost 4 games, how basketball games. If they lost 4 games, how many games have been played?many games have been played?

202.4

RP

B

Won = 80% Lost = 20%


Determining Rate of Increase or Determining Rate of Increase or DecreaseDecrease

amount Originalchange of Amount

Change of Rate


Rate of Increase or Decrease Rate of Increase or Decrease ExampleExample

• Allied Plumbing sold 2,390 feet of 5/8-inch galvanized Allied Plumbing sold 2,390 feet of 5/8-inch galvanized pipe in July. If 2,558 feet were sold in August, what is pipe in July. If 2,558 feet were sold in August, what is the percent increase in pipe footage sales?the percent increase in pipe footage sales?

168390,2558,2IncreaseP

%707.390,2168

BP

R

2,390Amount OriginalB


Rate of Increase or Decrease Rate of Increase or Decrease ExampleExample

• The supermarket price of yellow onions dropped from The supermarket price of yellow onions dropped from $.59 per pound to $.45 per pound. What is the percent $.59 per pound to $.45 per pound. What is the percent decrease in the price of onions?decrease in the price of onions?

14.0$49.0$59.0$DecreaseP

%73.232373.59.

14.

B

PR

59.0$Amount OriginalB


Determining the New Amount Determining the New Amount After a Percent ChangeAfter a Percent Change


Determining the New Amount AfterDetermining the New Amount Aftera Percent Change Examplea Percent Change Example

• Economists predict that next year housing prices Economists predict that next year housing prices will drop by 4%. This year’s price for an average will drop by 4%. This year’s price for an average house is $110,000. What will the average price house is $110,000. What will the average price of a house be next year?of a house be next year?

%96%4%100Rate

000,110Amount OriginalBase

600,105000,11096.BRP


Determining the Original Amount Determining the Original Amount Before a Percent ChangeBefore a Percent Change


Determining the Original Amount Determining the Original Amount Before a Percent Change ExampleBefore a Percent Change Example

• Metro Motors sold 112 cars this month. If this is Metro Motors sold 112 cars this month. If this is 40% better than last month, how many cars 40% better than last month, how many cars were sold last month?were sold last month?

cars 804.1

112RP

B

112Portion

4.1%140%40%100Rate


Determining the Original Amount Determining the Original Amount BeforeBefore

a Percent Change Example (cont’d)a Percent Change Example (cont’d)• The second shift of a factory produced 17,010 The second shift of a factory produced 17,010

units. If this amount was 5 ½% less than the units. If this amount was 5 ½% less than the first shift, how many units were produced on the first shift, how many units were produced on the first shift?first shift?

units 8,0001945.010,17

RP

B

010,17Portion

945.%094%5%100Rate 21

21


Problems Involving Percentage Problems Involving Percentage PointsPoints

• percentage pointspercentage points A way of expressing a change from an original A way of expressing a change from an original

amount to a new amount, without using a percent amount to a new amount, without using a percent sign.sign.

Rate of Rate of changechange ==

Change in percentage pointsChange in percentage points

Original amount of percentage pointsOriginal amount of percentage points



• After a vigorous promotion campaign, HiLo Mart After a vigorous promotion campaign, HiLo Mart increased its market share from 5.4% to 8.1%, a increased its market share from 5.4% to 8.1%, a rise of 2.7 percentage points. What percent rise of 2.7 percentage points. What percent increase in sales does this represent?increase in sales does this represent?

027.%7.2IncreasePortion

%505.054.027.

BP

change of Rate

054.%4.5Base



• The unemployment rate in Glen Haven dropped The unemployment rate in Glen Haven dropped from 8.8% to 6.8% in the past year, a decrease from 8.8% to 6.8% in the past year, a decrease of 2 percentage points. What percent decrease of 2 percentage points. What percent decrease does this represent?does this represent?

020.%0.2DecreasePortion

%73.222273.088.

020.change of

B

PRate

088.%8.8Base


Chapter Review Problem 1 Chapter Review Problem 1

• Solve the following by converting to a decimal:Solve the following by converting to a decimal:

%27 27.

%81. 0081.

%12 43 1275.%75.12

%523 0046.%6.4%4 5

3



• An ad read, “This week only, all merchandise An ad read, “This week only, all merchandise 35% off!” If a television set normally sells for 35% off!” If a television set normally sells for $349.95, what is the amount of the savings?$349.95, what is the amount of the savings?

%35Rate

95.349Amount OriginalBase

48.12295.34935.BRP



• If 453 runners out of 620 completed a marathon, If 453 runners out of 620 completed a marathon, what percent of the runners finished the race? what percent of the runners finished the race?

453Portion

%1.73731.620453

BP

R

620Amount OriginalBase



• By what percent is a 100-watt light bulb brighter By what percent is a 100-watt light bulb brighter than a 60-watt bulb?than a 60-watt bulb?

4060100IncreasePortion

%7.66667.6040

BP

R

60Amount OriginalBase



• A pre-election survey shows that the popularity A pre-election survey shows that the popularity of a presidential candidate has increased from of a presidential candidate has increased from 26.5 percent to 31.3 percent of the electorate, 26.5 percent to 31.3 percent of the electorate, an increase of 4.8 percentage points. What an increase of 4.8 percentage points. What percent increase does this represent?percent increase does this represent?

8.45.263.31IncreasePortion

%1.18181.5.268.4

BP

R

5.26Amount OriginalBase

PowerPoint Presentation by Charlie Cook The University of West Alabama © 2009 Cengage Learning. All rights reserved. Percents and Their Applications in.

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