Chapter 8

8-1 Relating Decimals, Fractions, and Percents

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpEvaluate.

1. 2.

3. 4.

13

1

3+

14

215

315

–712

312

4 5

7 2

123

1 4

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45

2145

or

Problem of the Day

A fast-growing flower grows to a height of 12 inches in 12 weeks by doubling its height every week. If you want your flower to be only 6 inches tall, after how many weeks should you pick it?

11 weeks

Course 3


Learn to relate decimals, fractions, and percents.

Course 3


Vocabulary

percent

Insert Lesson Title Here

Course 3


Percents are ratios that compare a number to 100.

RatioEquivalent Ratio with Denominator of 100 Percent

310

1234

3010050

10075

100

30%

50%

75%

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Think of the % symbol as meaning /100.

0.75 = 75% = 75/100

Reading Math

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To convert a fraction to a decimal, divide the numerator by the denominator.

18 = 1 ÷ 8 = 0.125

To convert a decimal to a percent, multiply by 100 and insert the percent symbol.

0.125 100 12.5%

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Find the missing ratio or percent equivalent for each letter a–g on the number line.

Additional Example 1: Finding Equivalent Ratios and Percents

1

10a: 10% =

10100

=

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b: 0.25 =14

= 25%

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c: 40% =40100

=2

5

4

10=

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d: 0.60 =35

= 60%

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e: 23

% =66 0.666 = 23

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f: 12

% =87 0.875 = 78

8751000

=

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g: 125% =125 100

=5

4=

1

41

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Try This: Example 1

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c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

a: 12

% =12 0.125 = 18

1251000

=

Try This: Example 1 Continued

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b: 25% =25100

=1

4


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


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c: 0.375 =38

= 37 %1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


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d: 50% =50100

=1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


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e: 0.625 =58

= 62 %1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


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f: 75% =75100

=3

4


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1


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g: 1 =100 100

= 100%


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Find the equivalent fraction, decimal, or percent for each value given on the circle graph.

Additional Example 2: Finding Equivalent Fractions, Decimals, and Percents

0.15(100) = 15%

720

= 0.35

Fraction Decimal Percent

0.15

35%

38%

320

15100

=

720

35100

=

1950

38100

= 1950 = 0.38

325 = 0.12 0.12(100) = 12%

325

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You can use information in each column to make three equivalent circle graphs. One shows the breakdown by fractions, one shows the breakdown by decimals, and one shows the breakdown by percents.

Additional Example 2 Continued

The sum of the fractions should be 1.

The sum of the decimals should be 1.

The sum of the percents should be 100%.

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Try This: Example 2

Fill in the missing pieces on the chart below.

Fraction Decimal Percent

0.1

45%

110 0.1(100) = 10%

0.2(100) = 20%

45100

=0.45

1 5

15

=0.2525100

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1 4

45100

920=

0.25(100) = 25%

= 0.2

Gold that is 24 karat is 100% pure gold. Gold that is 14 karat is 14 parts pure gold and 10 parts another metal, such as copper, zinc, silver, or nickel. What percent of 14 karat gold is pure gold?

Additional Example 3: Physical Science Application

Set up a ratio and reduce.parts pure goldtotal parts

1424

712

=

712

= 7 12 = Find the percent.0.583 = 58.3%

13So 14-karat gold is 58.3%, or 58 % pure

gold.

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A baker’s dozen is 13. When a shopper purchases a dozen items at the bakery they get 12. It is said that the baker eats 1 item from every batch. So, what percentage of the food the baker cooks is eaten without being sold?

Try This: Example 3

Set up a ratio and reduce. items eatentotal items

113

113

= 1 13 = Find the percent.0.077 = 7.7%

So the baker, eats 7.7% of the items they bake.

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Lesson Quiz

Find each equivalent value.

1. as a percent

2. 20% as a fraction

3. as a decimal

4. as a percent

5. About 342,000 km2 of Greenland’s total area (2,175,000 km2) is not covered with ice. To the nearest percent, what percent of Greenland’s total area is not covered with ice?

16%

37.5%


0.625

56%

38

1425

15

58

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8-2 Finding Percents

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Warm UpWarm Up



Warm UpRewrite each value as indicated.

1. as a percent

2. 25% as a fraction

3. as a decimal

4. 0.16 as a fraction

48%

0.375

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425

24 50

3 8

14

Problem of the Day

A number between 1 and 10 is halved, and the result is squared. This gives an answer that is double the original number. What is the starting number?8

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Learn to find percents.

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Relative humidity is a measure of the amount of water vapor in the air. When the relative humidity is 100%, the air has the maximum amount of water vapor. At this point, any additional water vapor would cause precipitation. To find the relative humidity on a given day, you would need to find a percent.

Additional Example 1A: Finding the Percent One Number Is of Another

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A. What percent of 220 is 88?

Method 1: Set up an equation to find the percent.

p 220 = 88 Set up an equation.

88220

p = Solve for p.

p = 0.4 0.4 is 40%.

So 88 is 40% of 220.

B. Eddie weighs 160 lb, and his bones weigh 24 lb. Find the percent of his weight that his bones are.

Additional Example 1B: Finding the Percent One Number Is of Another

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Think: What number is to 100 as 24 is to 160?

=number

100 partwhole

Set up a proportion.

Substitute. n

100 24160

=

n 160 = 100 24

160n = 2400

Find the cross products.

Method 2: Set up a proportion to find the percent.


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n = 15

= 15

100 24160

The proportion is reasonable.

Solve for n.160 2400n =

So 15% of Eddie’s weight is bone.

Try This: Example 1A

A. What percent of 110 is 11?


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Method 1: Set up an equation to find the percent.

p 110 = 11 Set up an equation.

11110

p = Solve for p.

p = 0.1 0.1 is 10%.

So 11 is 10% of 110.

B. Jamie weighs 140 lb, and his bones weigh 21 lb. Find the percent of his weight that his bones are.

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Think: What number is to 100 as 21 is to 140?

=number

100 partwhole Set up a proportion.

Substitute. n

100 21140

=

n 140 = 100 21

140n = 2100

Find the cross products.

Try This: Example 1B

Method 2: Set up a proportion to find the percent.

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n = 15

The proportion is reasonable.

Solve for n.140 2100n =

So 15% of Jamie’s weight is bone.

= 15

100 21140

Additional Example 2A: Finding a Percent of a Number

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A. After a drought, a reservoir had only 66 % of the average amount of water. If the average amount of water is 57,000,000 gallons, how much water was in the reservoir after the drought?

23

Choose a method: Set up an equation.

Think: What number is 66 % of 57,000,000?23

w = 66 % 57,000,000 Set up an equation.23

w = 57,000,000 66 % is equivalent to . 23

23

23

Additional Example 2A Continued

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The reservoir contained 38,000,000 gallons of water after the drought.

w = = 38,000,000 114,000,000

3

Additional Example 2B: Finding Percents

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B. Ms. Chang deposited $550 in the bank. Four years later her account held 110% of the original amount. How much money did Ms. Chang have in the bank at the end of the four years?

Choose a method: Set up a proportion.

=110

100 a

550Set up a proportion.

110 550 = 100 a Find the cross products.

60,500 = 100a

Additional Example 2B Continued

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605 = a Solve for a.

Ms. Chang had $605 in the bank at the end of the four years.


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A. After a drought, a river had only 50 % of the average amount of water flow. If the average amount of water flow is 60,000,000 gallons per day, how much water was flowing in the river after the drought?

23


Think: What number is 50 % of 60,000,000?23

w = 50 % 60,000,000 Set up an equation.23

w = 0.506 60,000,000 50 % is equivalent to 0.506. 23


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The water flow in the river was 30,400,000 gallons per day after the drought.

w = 30,400,000


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B. Mr. Downing deposited $770 in the bank. Four years later her account held 120% of the original amount. How much money did Mr. Downing have in the bank at the end of the four years?


=120

100 a

770 Set up a proportion.

120 770 = 100 a Find the cross products.

92,400 = 100a

Try This: Example 2B Continued

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924 = a Solve for a.

Mr. Downing had $924 in the bank at the end of the four years.

Lesson Quiz

Find each percent to the nearest tenth.

1. What percent of 33 is 22?


3. 18 is what percent of 25?

4. The volume of Lake Superior is 2900 mi3 and

the volume of Lake Erie is 116 mi3. What percent

of the volume of Lake Superior is the volume of

Lake Erie?

40%

66.7%


72%

4%

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8-3 Finding a Number When the Percent Is Known

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Warm UpWarm Up



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90%

12.5%

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625%

331

3 %

Problem of the Day

The original price of a sweater is $40. The sweater goes on sale for 75% of its original price. Later, the sweater goes on clearance for 50% of its sale price. What is the clearance price of the sweater?$15

Course 3


Learn to find a number when the percent is known.

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The Pacific giant squid can grow to a weight of 2000 pounds. This is 1250% of the maximum weight of the Pacific giant octopus. When one number is known, and is relationship to another number is given by a percent, the other number can be found.

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60 = 0.12n

60 is 12% of what number?

Additional Example 1: Finding a Number When the Percent Is Known

Set up an equation to find the number.

60 = 12% n

= n 60

0.12 0.12

0.12Divide both sides by 0.12.

500 = n

60 is 12% of 500.

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Set up an equation.

1210012% =

75 = 0.25n

75 is 25% of what number?

Try This: Example 1

Set up an equation to find the number.

75 = 25% n

= n 75

0.25 0.25

0.25 Divide both sides by 0.25.

300 = n

75 is 25% of 300.

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Set up an equation.

2510025% =

Anna earned 85% on a test by answering 17 questions correctly. If each question was worth the same amount, how many questions were on the test?

Additional Example 2: Application

Choose a method: Set up a proportion to find the number.

Think: 85 is to 100 as 17 is to what number?

= 85

10017

nSet up a proportion.

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There were 20 questions on the test.

85 n = 100 17 Find the cross products.

85 n = 1700

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n = Solve for n.1700

85

n = 20

Try This: Example 2

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Choose a method: Set up a proportion to find the number.


= 80

10020

nSet up a proportion.

Tom earned 80% on a test by answering 20 questions correctly. If each question was worth the same amount, how many questions were on the test?


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There were 25 questions on the test.

80 n = 100 20 Find the cross products.

80 n = 2000

n = Solve for n.2000

80

n = 25

A. A fisherman caught a lobster that weighed 11.5 lb. This was 70% of the weight of the largest lobster that fisherman had ever caught. What was the weight, to the nearest tenth of a pound, of the largest lobster the fisherman had ever caught?

Additional Example 3A: Life Science Application


Think: 11.5 is 70% of what number?

11.5 = 70% n Set up an equation.

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Additional Example 3A Continued

16.4 n

The largest lobster the fisherman had ever caught was about 16.4 lb.

11.5 = 0.70 n 70% = 0.70

Solve for n. 11.5 0.70

n=

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B. When a giraffe is born, is approximately 55% as tall as it will be as an adult. If a baby giraffe is 5.2 feet tall when it is born, how tall will it be when it is full grown, to the nearest tenth of a foot?

Additional Example 3B: Life Science Application


Think: 55 is to 100 and 5.2 is to what number?

= h

5.2 55 100


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55h = 520

This giraffe will be approximately 9.5 feet tall when full grown.

55 h = 100 5.2 Find the cross products.

52055

h = Solve for h.

h 9.5

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A. Amy caught a fish that weighed 15.5 lb. This was 85% of the weight of the largest fish that Amy had ever caught. What was the weight, to the nearest tenth of a pound, of the largest fish that Amy had ever caught?

Try This: Example 3


Think: 15.5 is 85% of what number?

15.5 = 85% n Set up an equation.

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18.2 n

The largest fish that Amy had ever caught was about 18.2 lb.

15.5 = 0.85 n 85% = 0.85

Solve for n. 15.5 0.85

n=

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B. When Bart was 12, he was approximately 85% of the weight he is now. If Bart was 120 lb, how heavy is he now, to the nearest tenth of a pound?

Try This: Example 3



= w

120 85 100


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85w = 12000

Bart weighs approximately 141.2 lbs.

85 w = 100 120 Find the cross products.

12000 85

w = Solve for h.

w 141.2

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Three Types of Percent Problems

1. Finding the percent of a number. 15% of 120 = n

2. Finding the percent one number is of another.p% of 120 = 18

3. Finding a number when the percent is known.15% of n = 18

You have now seen all three types of percent problems.

Lesson Quiz

1. 10 is 12 % of what number?

2. 326 is 25% of what number?

3. 44% of what number is 11?


5. Larry has 9 novels about the American

Revolutionary War. This represents 15% of his

total book collection. How many books does Larry

have in all?

1304

80


25

50

12

60

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8-4 Percent Increase and Decrease

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Warm UpWarm Up



Warm Up

1. 14,000 is 2 % of what number?

2. 39 is 13% of what number?

3. 37 % of what number is 12?


560,000

300

32

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12

126

12

Problem of the Day

In a school survey, 45% of the students said orange juice was their favorite juice, 25% preferred apple, and 10% preferred grapefruit. The remaining 32 students preferred grape juice. How many students participated in the survey?

160 students

Course 3


Learn to find percent increase and decrease.

Course 3


Vocabulary

percent changepercent increasepercent decrease


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Percents can be used to describe a change. Percent change is the ratio of the amount of change to the original amount.

Percent increase describes how much the original amount increases.

Percent decrease describes how much the original amount decreases.

amount of changeoriginal amountpercent change =

Find the percent increase or decrease from 16 to 12.

Additional Example 1: Percent Increase and Decrease

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This is percent decrease.

16 – 12 = 4 First find the amount of change.

Think: What percent is 4 of 16?

amount of decreaseoriginal amount

416

Set up the ratio.


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= 25% Write as a percent.

= 0.25 Find the decimal form.416

From 16 to 12 is a 25% decrease.

Find the percent increase or decrease from 15 to 20.

Try This: Example 1

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This is percent increase.



amount of increaseoriginal amount

520

Set up the ratio.


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= 0.25 Find the decimal form.520

From 15 to 20 is a 25% increase.

A. When Jim was exercising, his heart rate went from 70 beats per minute to 98 beats per minute. What was the percent increase?

Additional Example 2: Life Science Application

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28 70

Set up the ratio.




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= 0.4 Find the decimal form. 70

28

Jim’s heart rate increased by 40% when he exercised.

B. In 1999, a certain stock was worth $1.25 a share. In 2002, the same stock was worth $0.85 a share. What was the percent decrease?

Additional Example 2B: Application

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1.25 – 0.85 = 0.40 First find the amount of change.

Think: What percent is 0.40 of 1.25?

amount of decreaseoriginal amount 1.25

0.40Set up the ratio.


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= 0.32 Find the decimal form. 1.25

0.40

The value of the stock decreased by 32%.

A. When Jeff was watching TV, the number of times his eyelids blinked went from 50 blinks per minute to 75 blinks per minute. What was the percent increase?


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25 50

Set up the ratio.



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= 0.5 Find the decimal form. 50

25

The blinking of Jeff’s eyelids increased by 50% when he watched TV.

Try This: Example 2A Continued

B. In 2000, a certain stock was worth $9.00 a share. In 2003, the same stock was worth $3.80 a share. What was the percent decrease?


Course 3


9.00 – 3.80 = 5.20 First find the amount of change.

Think: What percent is 5.20 of 9.00?

amount of decreaseoriginal amount 9.00

5.20Set up the ratio.

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The value of the stock decreased by about 57.8%.

9.005.20 = 0.57 Find the decimal form.

= 57.7% Write as a percent.

Try This: Example 2B Continued

A. Sarah bought a DVD player originally priced at $450 that was on sale for 20% off. What was the sale price?

Additional Example 3A: Percent Increase and Decrease

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$450 20% First find 20% of $450.

$450 0.20 = $90 20% = 0.20

The amount of decrease is $90.

Think: The reduced price is $90 less than $450.

$450 – $90 = $360 Subtract the amount of decrease.The sale price of the DVD player was $360.

B. Mr. Olsen has a computer business in which he sells everything at 40% above the wholesale price. If he purchased a printer for $85 wholesale, what will be the retail price?

Additional Example 3B: Percent Increase and Decrease

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$85 40% First find 40% of $85.

$85 0.40 = $34 40% = 0.40

The amount of increase is $34.

Think: The retail price is $34 more than $85.

$85 + $34 = $119 Add the amount of increase.

The retail price of this printer will be $119.

A. Lily bought a dog house originally priced at $750 that was on sale for 10% off. What was the sale price?


Course 3


$750 10% First find 10% of $750.

$750 0.10 = $75 10% = 0.10

The amount of decrease is $75.

Think: The reduced price is $75 less than $750.

$750 – $75 = $675 Subtract the amount of decrease.

The sale price of the dog house was $675.

B. Barb has a grocery store in which she sells everything at 50% above the wholesale price. If she purchased a prime rib for $30 wholesale, what will be the retail price?

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$30 50% First find 50% of $30.

$30 0.50 = $15 50% = 0.50

The amount of increase is $15.

Think: The retail price is $15 more than $30.

$30 + $15 = $45 Add the amount of increase.

The retail price of the prime rib will be $45.


Lesson QuizFind each percent increase or decrease to the nearest percent.

1. from 12 to 15

2. from 1625 to 1400

3. from 37 to 125

4. from 1.25 to 0.85

5. A computer game originally sold for $40 but is

now on sale for 30% off. What is the sale price of

the computer game?

14% decrease

25% increase


238% increase

32% decrease

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$28

8-6 Applications of Percents

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Warm UpWarm Up



Warm UpEstimate.

1. 20% of 602

2. 133 out of 264

3. 151% of 78

4. 0.28 out of 0.95

120

50%

120

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30%

Possible answers:

Problem of the Day

What is the percent discount on a purchase of three shirts if you take advantage of the shirt sale?

All Shirts on Sale!Buy 2—Get the Third for Half Price!

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16 %2

3

Learn to find commission, sales tax, and withholding tax.

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Vocabulary

commissioncommission ratesales taxwithholding tax


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Course 3


Real estate agents often work for commission. A commission is a fee paid to a person who makes a sale. It is usually a percent of the selling price. This percent is called the commission rate.

Often agents are paid a commission plus a regular salary. The total pay is a percent of the sales they make plus a salary.

commission ratecommission rate salessales = commissioncommission

A real-estate agent is paid a monthly salary of $900 plus commission. Last month he sold one condominium for $65,000, earning a 4% commission on the sale. How much was his commission? What was his total pay last month?

Additional Example 1: Multiplying by Percents to Find Commission Amounts

Course 3


First find his commission.

4% $65,000 = c commission rate sales = commission

0.04 65,000 = c Change the percent to a decimal.


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2600 = c Solve for c.

He earned a commission of $2600 on the sale.

Now find his total pay for last month.

$2600 + $900 = $3500 commission + salary = total pay

His total pay for last month was $3500.

A car sales agent is paid a monthly salary of $700 plus commission. Last month she sold one sports car for $50,000, earning a 5% commission on the sale. How much was her commission? What was her total pay last month?

Try This: Example 1

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First find her commission.

5% $50,000 = c commission rate sales = commission

0.05 50,000 = c Change the percent to a decimal.


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2500 = c Solve for c.

The agent earned a commission of $2500 on the sale.

Now find her total pay for last month.

$2500 + $700 = $3200 commission + salary = total pay

Her total pay for last month was $3200.

Course 3


Sales tax is the tax on the sale of an item or service. It is a percent of the purchase price and is collected by the seller.

If the sales tax rate is 6.75%, how much tax would Adrian pay if he bought two CDs at $16.99 each and one DVD for $36.29?

Additional Example 2: Multiplying by Percents to Find Sales Tax Amounts

Course 3


CD: 2 at $16.99 $33.98

DVD: 1 at $36.29 $36.29

$70.27 Total Price

0.0675 70.27 = 4.743225 Convert tax rate to a decimal and multiply by the total price.

Adrian would pay $4.74 in sales tax.

Try This: Example 2

Amy rents a hotel for $45 per night. She rents for two nights and pays a sales tax of 13%. How much tax did she pay?


Course 3


$45 2 = $90 Find the total price for the hotel stay.

$90 0.13 = $11.70 Convert tax rate to a decimal and multiply by the total price.

Amy spent $11.70 on sales tax.

Course 3


A tax deducted from a person’s earnings as an advance payment of income tax is called withholding tax.

Anna earns $1500 monthly. Of that, $114.75 is withheld for Social Security and Medicare. What percent of Anna’s earnings are withheld for Social Security and Medicare?

Additional Example 3: Using Proportions to Find the Percent of Tax Withheld

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Think: What percent of $1500 is $114.75?

Solve by proportion:

114.75 1500

n100

=

n 1500 = 100 114.75Find the cross products.


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n = 7.65

7.65% of Anna’s earnings is withheld for Social Security and Medicare.

11,475 1500

n =

1500n = 11,475 Divide both sides by 1500.

BJ earns $2500 monthly. Of that, $500 is withheld for income tax. What percent of BJ’s earnings are withheld for income tax?

Try This: Example 3

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Think: What percent of $2500 is $500?

Solve by proportion:

500 2500

n100

=

n 2500 = 100 500 Find the cross products.


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n = 20

20% of BJ’s earnings are withheld for income tax.

50000 2500

n =

2500n = 50,000 Divide both sides by 2500.

A furniture sales associate earned $960 in commission in May. If his commission is 12% of sales, how much were his sales in May?

Additional Example 4: Dividing by Percents to Find Total Sales

Course 3


Think: $960 is 12% of what number?

Solve by equation:

960 = 0.12 s Let s = total sales.

9600.12

= s Divide each side by 0.12.

The associate’s sales in May were $8000.

A sales associate earned $770 in commission in May. If his commission is 7% of sales, how much were his sales in May?

Try This: Example 4

Course 3


Think: $770 is 7% of what number?

Solve by equation:

770 = 0.07 s Let s represent total sales.

7700.07

= s Divide each side by 0.07.

The associate’s sales in May were $11,000.

Lesson Quiz: Part 1

1. The lunch bill was $8, and you want to leave a 15% tip. How much should you tip?

2. The sales tax is 5.75%, and the shirt costs $20. What is the total cost of the shirt?

3. As of 2001, the minimum hourly wage was $5.15. Congress proposed to increase it to $6.15 per hour. To the nearest percent, what is the proposed percent increase in the minimum wage?

$21.15

$1.20


Course 3


19%

Lesson Quiz: Part 2

4. It costs a business $13.30 to make its product. To satisfy investors, the company needs to make $4 profit per unit. To the nearest percent, what should be the company’s markup?


30%

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8-7 More Applications of Percents

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Warm UpWarm Up



Warm Up

1. What is 35 increased by 8%?

2. What is the percent of decrease from 144 to 120?

3. What is 1500 decreased by 75%?

4. What is the percent of increase from 0.32 to 0.64?

37.8

375

Course 3


100%

16 %2

3

Problem of the Day

Maggie is running for class president. A poll revealed that 40% of her classmates have decided to vote for her, 32% have decided to vote for her opponent, and 7 voters are undecided. If she needs 50% of the vote to win, how many of the undecided voters must vote for Maggie for her to win the election? 3

Course 3


Learn to compute simple interest.

Course 3


Vocabulary

interestsimple interestprincipalrate of interest


Course 3


Course 3


When you borrow money from a bank, you pay interest for the use of the bank’s money. When you deposit money into a savings account, you are paid interest. Simple interest is one type of fee paid for the use of money.

I = P r t

Simple Interest

Principal is the amount of money borrowed or invested

Rate of interest is the percent charged or earned

Time that the money is borrowed or invested (in years)

To buy a car, Jessica borrowed $15,000 for 3 years at an annual simple interest rate of 9%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay?

Additional Example 1: Finding Interest and Total Payment on a Loan

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First, find the interest she will pay.

I = P r t Use the formula.

I = 15,000 0.09 3 Substitute. Use 0.09 for 9%.

I = 4050 Solve for I.


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Jessica will pay $4050 in interest.

P + I = A principal + interest = amount

15,000 + 4050 = A Substitute.

19,050 = A Solve for A.

You can find the total amount A to be repaid on a loan by adding the principal P to the interest I.

Jessica will repay a total of $19,050 on her loan.

To buy a laptop computer, Elaine borrowed $2,000 for 3 years at an annual simple interest rate of 5%. How much interest will she pay if she pays the entire loan off at the end of the third year? What is the total amount that she will repay?

Try This: Example 1

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First, find the interest she will pay.


I = 2,000 0.05 3 Substitute. Use 0.05 for 5%.



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Elaine will pay $300 in interest.

P + I = A principal + interest = amount

2000 + 300 = A Substitute.

2300 = A Solve for A.

You can find the total amount A to be repaid on a loan by adding the principal P to the interest I.

Elaine will repay a total of $2300 on her loan.

Additional Example 2: Determining the Amount of Investment Time

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450 = 6,000 0.03 t Substitute values into the equation.

2.5 = t Solve for t.

Nancy invested $6000 in a bond at a yearly rate of 3%. She earned $450 in interest. How long was the money invested?

450 = 180t

The money was invested for 2.5 years, or 2 years and 6 months.

Try This: Example 2

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200 = 4,000 0.02 t Substitute values into the equation.

2.5 = t Solve for t.

TJ invested $4000 in a bond at a yearly rate of 2%. He earned $200 in interest. How long was the money invested?

200 = 80t

The money was invested for 2.5 years, or 2 years and 6 months.

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I = 1000 0.0325 18 Substitute. Use 0.0325 for 3.25%.


Now you can find the total.

Additional Example 3: Computing Total Savings

John’s parents deposited $1000 into a savings account as a college fund when he was born. How much will John have in this account after 18 years at a yearly simple interest rate of 3.25%?

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P + I = A Use the formula.

1000 + 585 = A

1585 = A

John will have $1585 in the account after 18 years.


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I = 1000 0.075 50 Substitute. Use 0.075 for 7.5%.


Now you can find the total.

Try This: Example 3

Bertha deposited $1000 into a retirement account when she was 18. How much will Bertha have in this account after 50 years at a yearly simple interest rate of 7.5%?

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1000 + 3750 = A

4750 = A

Bertha will have $4750 in the account after 50 years.


Mr. Johnson borrowed $8000 for 4 years to make home improvements. If he repaid a total of $10,320, at what interest rate did he borrow the money?

Additional Example 4: Finding the Rate of Interest

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8000 + I = 10,320

I = 10,320 – 8000 = 2320 Find the amount of interest.

He paid $2320 in interest. Use the amount of interest to find the interest rate.


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2320 = 32,000 r Multiply.


2320 = 8000 r 4 Substitute.

232032,000

= r Divide both sides by 32,000.

0.0725 = r

Mr. Johnson borrowed the money at an annual rate

of 7.25%, or 7 %.14

Mr. Mogi borrowed $9000 for 10 years to make home improvements. If he repaid a total of $20,000 at what interest rate did he borrow the money?

Try This: Example 4

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9000 + I = 20,000

I = 20,000 – 9000 = 11,000 Find the amount of interest.

He paid $11,000 in interest. Use the amount of interest to find the interest rate.


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11,000 = 90,000 r Multiply.


11,000 = 9000 r 10 Substitute.

11,000 90,000

= r Divide both sides by 90,000.

0.12 = r

Mr. Mogi borrowed the money at an annual rate of about 12.2%.

Lesson Quiz: Part 1

1. A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in one year?

2. Joshua borrowed $1000 from his friend and paid him back $1050 in six months. What simple annual interest did Joshua pay his friend? 10%

$125


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Lesson Quiz: Part 2

3. The Hemmings borrowed $3000 for home improvements. They repaid the loan and $600 in simple interest four years later. What simple annual interest rate did they pay?

4. Mr. Berry had $120,000 in a retirement account. The account paid 4.25% simple interest. How much money was in the account at the end of 10 years?


5%

$171,000

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Chapter 8

Technology

Transcript of Chapter 8