Module3

Types of Strategies to Solve Percentage ProblemsBy: Kari Knisely

What you will learn…

When and how to use the following strategies:

10% Rule

Percent Proportion

Percent Equation

Percent of Change Equation

Tic-Tac-Toe Table

What you will need…

Take notes as needed in order to familiarize yourself with the strategies presented.

Pencil

Paper

10% Rule

When given an amount before a change (known as a whole or starting amount such as Original price before increase/decrease Subtotal before tax or tip Total amount of questions possible on a test)

, then use 10% rule to estimate your answer

10% Rule

Move the decimal 1 place to the left

10% of 40

10% of

32.6

10% of 2

10% of

5,345

= 4.0

= 3.26

= .2

= 534.5

10% Rule – Example 1

40% of 25 = ? 10% of 25 = 2.510% of 25 = 2.5

10% of 25 = 2.5

10% of 25 = 2.5

40% of 25

= 10.0

0% 100%50%25% 75%

0 2512.5

6.25

18.75

10

40%

10% Rule –Example 2

30% of 30 = ? 10% of 30 = 3.010% of 30 = 3.010% of 30 = 3.030% of 30

= 9.0

0% 100%50%25% 75%

0 30157.5

22.5

9.0

30%

10% Rule –Example 3

20% of 795 = ?

10% of 795 = 79.510% of 795 = 79.520% of 795

=159.0

0% 100%50%25% 75%

7950 397.5

198.75 596.25

20%

159

Problems when you can apply the 10% Rule

Amount before a change

Can you apply the 10% Rule to these type of problems?

Amount before change

What was the subtotal?



Amount after a change



How much total will you leave?

Subtotal$9.00



Subtotal $9.00

10% of 9.00 = 0.905% of 9.00 = 0.4515% of 9.00 = 1.35Subtotal $ 9.00Tip 1.35Total $10.35




Percent after a change



Subtotal $8.59

Total $12.00(including tip, exclude sales tax)


Subtotal $8.59Total $12.00(including tip only… ignore sales tax)

10% of $8.59 = .859 = .86

100% Starting Price $8.59

10% of $8.59 = .859 = .86120% $10.3110% of $8.59 = .859 = .86130% $11.1710% of $8.59 = .859 = .86140% $12.03

When you can apply the 10% Rule




Percent of change


Percentage of Change

Subtotal $8.59

Total $12.00(including tip and 6% sales tax)


Subtotal $8.59Total $12.00(including tip only… ignore sales tax)

Starting Price $8.59+10% of $8.59 = .859 = .86+10% of $8.59 = .859 = .8620% $10.31+10% of $8.59 = .859 = .8630% $11.17+10% of $8.59 = .859 = .8640% $12.03





Percent of change

Amount of change

Amount of Change

Subtotal $8.59

Total $12.00(including tip and 6% sales tax)

Must be able to identify parts and whole to use

Need to have 3 of 4 pieces of information

Percent Proportion

Percent Proportion

PartWhole

%100

=isof

%100

=Non Percentage Amount

Non Percentage Amount

Percentage Amount

Percentage Amount

Percent Proportion – Example 1

40% of 25 = ?

0% 100%50%25% 75%

0 2512.5

6.25

18.75

10

40%

isof

%100

=

X25

40100

=

100 X = 25 40100X = 1000

X = 10


30% of ? is 9

0% 100%50%25% 75%

0 30157.5

22.5

9.0

30%

isof

= %100

9X= 30100

100 9 = X 30900 = 30X

30 = X


159 is ? % of 795

0% 100%50%25% 75%

7950 397.5

198.75 596.25

20%

159

isof

= %100

159795

= X100

100 159 = 795 X15900 = 795X

20 = X

Can you use the Percent Proportion to solve these type of problems?




Percent of change

Amount of change


What was the original price?

100 (20-X) = X -202000 – 100X = -

20X2000 = 80X25 = X


What price will you pay?

$30.00

100 X = 30 25 100X = 750

X = 7.50 $30.00 + 7.50$37.50


100 -5 = 30 -X-500 = -30X

16.6 = X

100% - 16.6% = 83.3%

Original $30.00

Total $25.00(after discount)

Percent of Change

100 -5 = 30 -X-500 = -30X

16.6 = X

Original $30.00

Total $25.00(after discount)

Amount of Change

Original $30.00

40% discount100 X = 30 -40100X = -1200

X = -12

$12.00

Percent Equation

% Whole = Part

Can you use the Percent Equation to solve these type of problems?




Percent of change

Amount of change


How many questions were on the test?

% Whole = Part .80 x = 42

.80x = 42x = 52.5

Approx 53 questions


How many questions were correct?

% Whole = Part

33.6 = X

.80 42 = X

Approx 34 questions


What percent of the questions were answered correctly?

% Whole = Part% 42 = 35

% = .83

83%


What percent of the questions were answered incorrectly?

% Whole = Part% 42 = 35

% = .83

100% - 83% = 17%

Amount of Change

How many questions were answered incorrectly?

% Whole = Part.83 42 = x

34.86= x42 – 34.86 =

7.14 Approx 7 questions

Percent of Change Equation – Example 1

New – Old

Old

= Percent of Change (as a decimal)

Can you use the Percent of Change Equation to solve these type of problems?




Percent of change

Amount of change


What was the original price if purchased in FL?

New – Old Old =

Percent of Change 59.95

- X X

= .06= .06X

59.95

1.06X

59.95 – X =

X=$56.56


What is the total price after tax?

New – Old Old = Percent

of ChangeX –

59.99 59.99

= .06

3.60X – 59.95

=X

$63.55

=


Original $79.99Total $62.00(after discount and sales tax)

New – Old Old

=% of Chg

62.00 – 79.99

79.99

=-0.2249

-0.2249 X 100 = -22.5%100% + -22.5% = 77.5%


Original $79.99Total $84.49(after sales tax)

*Sale was not in FL

New – Old Old =

% of Chg

84.49 – 79.99

79.99

= .05625

.05625X 100 5.63%

Amount of Change

Original $79.99

*FL Sales Tax is 6%

New – Old Old

= Percent of Change

X – 79.99 79.99

= .06

X – 79.99 = 4.80

X = 84.79

84.79 – 79.99

= $4.80

Tic-Tac-Toe

Whole/Original

Change (+ or -)

Part of Original

100

%

%

Start

+ or -

End

Can you use the Tic-Tac-Toe strategy to solve these type of problems?




Percent of change

Amount of change

Tic-Tac-Toe

Whole/Original

Change (+ or -)

Part of Original

100 %

%

%

Start

+ or -

End

AMOUNT PERCENT

Original starting amount before change

Amount of Change

Percent of Change

Ending amount after change

Ending percent after change

Tic-Tac-Toe

Whole/Original

Change (+ or -)

Part of Original

100 %

%

%

Start

+ or -

End

AMOUNT PERCENT

$40.00-

$8.00

-20

$32.00

80

40100

3280

-8-20

Tic-Tac-Toe

Whole/Original

Change (+ or -)

Part of Original

100 %

%

%

Start

+ or -

End

AMOUNT PERCENT

$40.00-

$8.00

-20

$32.00

80

10040

8032

-20-8

Tic-Tac-Toe

Whole/Original

Change (+ or -)

Part of Original

100 %

%

%

Start

+ or -

End

AMOUNT PERCENT

$40.00-

$8.00

-20

$32.00

80

4032

-832

-2080

10080

40-8

100-20

Tic-Tac-Toe

Whole/Original

Change (+ or -)

Part of Original

100 %

%

%

Start

+ or -

End

AMOUNT PERCENT

$40.00-

$8.00

-20

$32.00

80

3240

32-8

80-20

80100

-840

-20100

Tic-Tac-Toe

Whole/Original

Change (+ or -)

Part of Original

100 %

%

%

Start

+ or -

End

AMOUNT PERCENT

$40.00-

$8.00

-20

$32.00

80

-20-8

-20-8

100X

80XX=40 X=32

Tic-Tac-Toe

Whole/Original

Change (+ or -)

Part of Original

100 %

%

%

Start

+ or -

End

AMOUNT PERCENT

$40.00-

$8.00

-20

$32.00

80

40100

40100

-8X

32X X=80 X=-20


What was the subtotal?

$15.00

+18

118

?

X100

15118

118X = 1500X = 12.71

12.71

+2.29



Subtotal

$9.00

$9.00

+15

115

?

9100

x115

100X = 1035X = 10.35

$10.35

+1.35


Subtotal $8.59 Total $12.00

(including tip ONLY)

$8.59

$12.00 ?

8.59100

12X

8.59X = 1200X = 139.70

+3.41

139.70

+39.7




$8.59

$12.00

?

8.59100

3.41X

8.59X = 341X = 39.70

+3.41 +39.70

139.7

Amount of Change



$8.59

$12.00

?

12.00 – 8.59= 3.41

+3.41

What you learned…

When and how to use the following strategies:

10% Rule

Percent Proportion

Percent Equation

Percent of Change Equation

Tic-Tac-Toe Table

Works Cited

All images retrieved from Google images

Business

Module3