copyright © 2011 pearson education, inc. publishing as prentice hall. 6.3 solving percent problems...
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Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
6.3
Solving Percent Problems with
Equations
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 22
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.
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 33
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Translating to an Equation
Example:Translate to an equation: 60 is what percent of 40?
60 what percent of 40
60 = x 40?
is
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 44
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Translating to an Equation
Example:Translate to an equation: What number is 18% of 66?
What number 18% of 66?
x = 18% 66
is
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 55
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Translating to an Equation
Example:Translate to an equation: 25% of 68 is what number?
25% 68% is what number?
25% 68% = x?
of
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 66
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Remember that an equation is simply a mathematical statement that contains an equal sign ().
6 18x
equal sign
Helpful Hint
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 77
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
20% of 50 10
20% • 50 10percent base amount
Percent Equationpercent ∙ base amount
Solving Percent Problems
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 88
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
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.
Helpful Hint
Martin-Gay, Prealgebra & Introductory Algebra, 3ed 99
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Solving Percent Problems for the Amount
Example:What number is 9% of 65?
n = 9% 65
n = 0.09 65
n = 5.85
5.85 is 9% of 65.
What number is 9% of 65?
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Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1010
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Solving Percent Problems for the Base
Example:36 is 6% of what number?
36 = 6% x
36 is 6% of what number
36 = 0.06n36 0.06 =
0.06 0.06n
600 = n
36 is 6% of 600.
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Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1111
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Solving Percent Problems for the Percent
Example:24 is what percent of 144?
24 = x 144
24 is what percent of 144?
24 = 144x24 144 =
144 144x
0.16 = x216 % = 3
x
224 is 16 % of 144.3
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Martin-Gay, Prealgebra & Introductory Algebra, 3ed 1212
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.
Use the following to see if your answers are reasonable.
a percent greater than 100%
a percent less than 100%
a number larger than the original number
a number less than the original number
100% of a number the number
Helpful Hint