Math 015 Section 8.2 Percent Equations

1
Math 015 Section 8.2 Percent Equations
2
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
amount
percent

base
100
3
Obj To solve equations involving percents
Remember what the following words mean in percent
equations
what of is
What is written as an unknown
of indicates multiplication
is is written as an equal sign
4
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 3400
4 of 85,000 is 3400
5
Obj To solve equations involving percents
Example What is 8.7 of 160
x
8.7

160
100
100 x 1392
x 13.92
8.7 of 160 is 13.92
6
Obj To solve equations involving percents
14
Example Find 15 of 400
14
x
15

100
400
100 x 6100
x 61
14
15 of 400 is 61
7
Obj To solve equations involving percents
23
Example What is 16 of 66
23
16
x

66
100
100 x 1100
x 11
23
16 of 66 is 11
8
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 30
Answer 2470 phones were not defective
9
Obj To solve application problems
A workers 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 1.88
10
Obj To solve equations involving percents
Example 24 is what percent of 60


x
60
24
24 x 60 100

60 x 2400
x 40
24 is 40 of 60
11
Obj To solve equations involving percents
Example What percent of 40 is 30 ?
30

x

40
x 30 100 40

40 x 3000
x 75
30 is 75 of 40
12
Obj To solve application problems
The monthly payment for the Kaminski family is
787.50. What percent of the Kaminskis 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 21
Answer House payment is 21 of the income
13
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 22.988
Answer About 23 of the households were
watching
14
Obj To solve equations involving percents
Example 18 of what is 900

x
900
18

18 900 100 x

18 x 90,000
x 5000
18 of 5000 is 900
15
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 600
15 is 2.5 of 600
16
Obj To solve application problems
A used car has a value of 10,458 which is 42 of
the cars original value. What was the cars
original value ?
Strategy 10,458 is 42 of what ?
10,458 42 x
42
10,458

100
x
42 x 1,045,800
x 24,900
Answer The original value is 24,900
17
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 112
Original price
Answer The difference is 22.40