Transcript mgpia3e_ppt_06_03

6.3
Solving Percent
Problems with
Equations
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Key Words
of means multiplication (∙)
is means equals (=)
what (or some equivalent) means the unknown
number
Let x stand for the unknown number.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Translating to an Equation
Example:
Translate to an equation: 60 is what percent of 40?
60
is
what percent
of
40
60
=
x

40?
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Translating to an Equation
Example:
Translate to an equation: What number is 18% of 66?
What number
is
18%
of
66?
x
=
18%

66
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
4
Translating to an Equation
Example:
Translate to an equation: 25% of 68 is what number?
25%
of
68%
is
what number?
25%

68%
=
x?
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Helpful Hint
Remember that an equation is simply a mathematical
statement that contains an equal sign (=).
6 = 18x
equal sign
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Solving Percent Problems
20%
20%
percent
of 50
=
10
• 50 = 10
base
amount
Percent Equation
percent ∙ base = amount
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Helpful Hint
When solving a percent equation, write the percent
as a decimal or fraction.
If your unknown in the percent equation is a
percent, don’t forget to convert your answer to a
percent.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Solving Percent Problems for the Amount
Example:
What number is 9% of 65?
What number is 9% of 65?
n
= 9%
n
= 0.09 • 65
n
= 5.85
• 65
5.85 is 9% of 65.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
9
Solving Percent Problems for the Base
Example:
36 is 6% of what number?
36 is 6% of what number
36 = 6%
•
x
36 = 0.06n
36
0.06n
=
0.06
0.06
600 = n
36 is 6% of 600.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
10
Solving Percent Problems for the Percent
Example:
24 is what percent of 144?
24 is what percent of 144?
24 =
24 = 144x
24
144x
=
144
144
0.16 = x
2
16 % = x
3
• 144
x
2
24 is 16 % of 144.
3
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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Helpful Hint
Use the following to see if your answers are reasonable.
100% of a number = the number
a percent greater than =
100%
a percent less than
100%
=
a number larger than the
original number
a number less than the
original number
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed
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