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. Remember what the following words mean in percent equations
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 x = 4%
85,000
x 85,000 =
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
8.7 x =
100
160
100 x = 1392
x =
8.7% of 160 is

6. Obj: To solve equations involving percents14
Example: Find % of 400 14 x 15 =
400
100
100 x = 6100
x = 61 14
15 % of is 61

7. Obj: To solve equations involving percents
Example: What is % of 66 23 23 16 x = 66
100
100 x = 1100
x = 11
16 % of 66 is 11 23

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: find the number of defective phones subtract that number from 2500
Defective phones: What is 1.2% of 2500 x
1.2 =
2500
100
100 x = 3000
x = 30
Answer: phones were not defective

9. Obj: To solve application problems
A worker’s hourly wage was $23.50 before an 8% raise. What is the new hourly wage?
Strategy: find 8% of $ add that amount to the original wage
What is 8% of $23.50 x =
100x = 188
New wage = $25.38
x = 1.88

10. Obj: To solve equations involving percents
Example: is what percent of 60 24 =
x % 60 x =
60 x =
x = 40
24 is 40% of 60

11. Obj: To solve equations involving percents
Example: What percent of 40 is 30 ? x% 40 = 30 x =
40 x =
x = 75
30 is 75% of 40

12. Obj: To solve application problems
The monthly payment for the Kaminski family is $ What percent of the Kaminski’s monthly income of $3750 is the house payment ?
Strategy: What percent of $3750 is $ ?
x% · = x =
3750 x = 78,750
x = 21
Answer: House payment is 21% of the income

13. Obj: To solve application problems
On one Monday night, million of the approximately million households watching television were not watching David Letterman. What percent of the households were watching Letterman? Round to the nearest percent.
40.76 – = 9.37 million were watching
What percent of is 9.37 ?
x% · = 9.37 x =
40.76 x = 937
x »
Answer: About 23% of the households were watching

14. Obj: To solve equations involving percents
Example: % of what is 900 x
18% =
900 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 car’s original value. What was the car’s original value ?
Strategy: ,458 is 42% of what ?
10,458 = 42% · x
10,458 42 = x
100
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: is 80% of what
89.60 = 80% · x
2. subtract $89.60 from that answer x =
80 x = 8960
x = $112
Original price
Answer: The difference is $22.40