Percents

In Algebra County

Things to remember:

Of means multiply

To convert a decimal to a percent, movethe decimal two places to the right.

To convert a percent to a decimal, movethe decimal two places to the left.

To convert a percent to a fraction, divide by 100 .

45% of 30 45% 30

45% .45

30%.3

51%51

100

Use the basic equation below to solve percent problems:

% Amount Answer Example 1:What is 50% of 16? 50

16100

x or .50 16x Use a calculator to find the answer.

Example 2:What percent of 14 is 8? 14 8

100

x

14 8

100 1

x

14 800x 14 14

57.1%x

If I spend 35% of my money, how much did I not spend?

65%.

With percents, 100% is an important concept.

Concept:

Example 3: (Easy)If 20% of p is 10, then 10% of p isA. 2B. 4C. 5D. 8E. 14

2010

100p

20 10

100 1

p

20 1000p

50p

10?

100p

10(50) 5

100

20 20

Example 4: (Medium)Mabel agreed to pay the tax and tip for dinner at a restaurant with her four friends. Each of the friends paid an equal part of the cost of the dinner, which was $96. If the tax and tip together were 20% of the cost of the meal, Mabel paid how much less than any one of her other friends?A.$2.40B.$4.80C.$9.20D.$19.20E.$24.00

Mabel’s friends paid each. This makes $24 each.

96 4

Mabel paid 20% of 96.

.20 96 19.20

Mabel $24 – $19.20 less than the others, which is $4.80

Example 5: (Hard)If 200% of 40% of x is equal to 40% of y, then x is what percent of y?A. 10%B. 20%C. 30%D. 50%E. 80%

200 40 40

100 100 100x y

8000 40

10000 100

x y

4 2

5 5

x y

(Reduce)

20 10x y

10

20x y

1

2x yOne-half is 50%.

Example 6: (Medium)A store owner buys a pound of grapes for 80 cents and sells it for a dollar. What percent of the selling price of grapes is the store owner’s profit?A. 10%B. 20%C. 25%D. 40%E. 80%

%x selling price profit

80 20100

x

80 20

100 1

x

80 2000x

25%x

80 80

Example 7: (Hard)On the first test of the semester, Barbara scored a 60. On the last test of the semester, she scored a 75. By what percent did Barbara’s score improve?A. 12%B. 15%C. 18%D. 20%E. 25%

%x first score improvement

60 15100

x

6015

100

x

3 15

5 1

x

3 75x

25%x

(Reduce)

3 3

Example 8: (Hard)Randy’s chain of used car dealerships sold 16,400 cars in 1998. If the chain sold 15,744 cars in 1999, by what percent did the number of cars sold decrease?A. 1%B. 4%C. 11%D. 40%E. 65%

% 1998x cars in decreaseincars

16,400 656100

x

16400 656

100 1

x

164 656

1 1

x

164 656x 164 164

4%x

Percent of increase or decrease is used in a lot of real life applications. For instance, an employee is expecting a 3% raise for next year. This means his new salary is 103% of what it was.Similarly, if his salary decreased 5%, he is making 95% of what he made last year.

Example 9: (Hard)Mr. White deposited a sum of money in an account at 4% annual interest. If his sum increased to $546 at the end of the year, how many dollars had he originally deposited?A. $525B. $515C. $520D. $502.50E. $510

The amount of money he has at the end of the year is 104% of what he started with.

104% starting amount final amount 104

546100

x

104 546

100 1

x

104 54600x 104 104

$525x

Percent of increase.

%x original amount amount of increase

Example 10: Erin received a raise at her job from $14 per hour to $17 per hour. What is the percent increase of her raise?

14 3100

x

14 3

100 1

x

14 300x 14 14

21.4%x

Keep Driving in Algebra County, even though

sometimes the work is hard.