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Math 009 Unit 5 Lesson 6PowerPoint Presentation

Math 009 Unit 5 Lesson 6

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Obj: To solve equations involving percents

Most percent problems that we will be working with can be written in the form:

amount

=

percent

·

base

This statement can be changed into the proportion

percent

amount

=

base

100

Obj: To solve equations involving percents

Because most of the problems will be written in words, you need to get used to some of the terminology and what the words mean

What is written as an unknown, (x)

of indicates multiplication

is is written as an equal sign

Obj: To solve equations involving percents

Example: What is 4% of $85,000

·

=

4%

85,000

x

x 85,000

4 100

=

100 x = 340,000

x = 340,000 ¸100

x = $3400

Obj: To solve equations involving percents

Example: What is 8.7% of 160

x

8.7

=

160

100

100 x = 1392

x = 1392 ¸ 100

x = 13.92

Obj: To solve equations involving percents

14

Example: Find 15 % of 400

14

x

15

=

100

400

100 x = 6100

x = 6100 ¸ 100

x = 61

Obj: To solve equations involving percents

23

Example: What is 16 % of 66

23

16

x

=

66

100

100 x = 1100

x = 1100 ¸ 100

x = 11

Obj: To solve equations involving percents

Remember what the following words mean in percent equations

whatof is

What is written as an unknown

of indicates multiplication

is is written as an equal sign

Obj: To solve equations involving percents

Example: 24 is what percent of 60

·

=

x %

60

24

24 x 60 100

=

60 x = 2400

x = 2400 ¸ 60

%

x = 40

Obj: To solve equations involving percents

Example: What percent of 40 is 30 ?

x%

·

40

=

30

x 30 100 40

=

40 x = 3000

x = 3000 ¸ 40

%

x = 75

Obj: To solve application problems

The monthly payment for the Kaminski family is $787.50. What percent of the Kaminski’s monthly income of $3750 is the house payment ?

Strategy: What percent of $3750 is $787.50 ?

x% · 3750 = 787.50

x 787.50 100 3750

=

3750 x = 78,750

x = 78,750 ¸ 3750

x = 21

Answer: House payment is 21% of the income

Obj: To solve application problems

On one Monday night, 31.39 million of the approximately 40.76 million households watching television were not watching David Letterman. What percent of the households were watching Letterman? Round to the nearest percent.

40.76 – 31.39 = 9.37 million were watching

What percent of 40.76 is 9.37 ?

x% · 40.76 = 9.37

x 9.37 100 40.76

=

40.76 x = 937

x = 937 ¸ 40.76

x » 22.988

Answer: About 23% of the households were watching

Obj: To solve equations involving percents

Example: 18% of what is 900

·

x

900

18%

=

18 900 100 x

=

18 x = 90,000

x = 90,000 ¸ 18

x = 5000

Obj: To solve equations involving percents

15 is 2.5 % of what ?

15 = 2.5% x

·

15

2.5

=

x

100

2.5 x = 1500

x = 1500 ¸ 2.5

x = 600

Obj: To solve application problems

A used car has a value of $10,458 which is 42% of the car’s original value. What was the car’s original value ?

Strategy: 10,458 is 42% of what ?

10,458 = 42% · x

10,458

42

=

x

100

42 x = 1,045,800

x = 1,045,800 ¸ 42

x = 24,900

Answer: The original value is $24,900

Obj: To solve application problems

A store has a tennis racket on sale for $89.60 which is 80% of the original price. What is the dollar difference between the original price and the sale price ?

Strategy: 1. 89.60 is 80% of what

89.60 = 80% · x

2. subtract $89.60 from that answer

89.60 80 x 100

=

80 x = 8960

x = 8960 ¸ 80

x = $112

Original price

Answer: The difference is $22.40

Obj: To solve application problems

A quality control inspector found that 1.2 % of 2500 telephones inspected were defective. How many telephones inspected were not defective.

Strategy: 1. find the number of defective phones 2. subtract that number from 2500

Defective phones: What is 1.2% of 2500

x

1.2

=

2500

100

100 x = 3000

x = 3000 ¸ 100

x = 30

Answer: 2470 phones were not defective

Obj: To solve application problems

A worker’s hourly wage was $23.50 before an 8% raise. What is the new hourly wage?

Strategy: 1. find 8% of $23.50 2. add that amount to the original wage

What is 8% of $23.50

x 8 23.50 100

=

100x = 188

New wage 23.50 + 1.88 = $25.38

x = 188 ¸ 100

x = 1.88

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