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§ 5.3A
Solving Percent
Problems Using
Equations
© 2010 Pearson Prentice Hall. All rights reserved
Percent Problems into Equations
To solve a percent problem, we express it as an
equation with an unknown quantity.
The following table is helpful when translating from
a percent problem to an equation.
Word
of
is
Mathematical Symbol
what
find
Any letter, for example, n
n=
Multiplication symbol:  or ( ) or ·
=
Tobey & Slater, Basic College Mathematics, 6e
2
Percent Problems into Equations
Example:
Translate into an equation.
What is 9% of 65?
n
= 9%  65
Example:
Translate into an equation.
24 is what percent of 144?
24 =
n
 144
Tobey & Slater, Basic College Mathematics, 6e
3
Solving a Percent Problem
A percent problem has three different parts.
amount = percent  base
Any one of the three quantities may be unknown.
1. When we do not know the amount:
n = 10%  500
2. When we do not know the base:
50 = 10%  n
3. When we do not know the percent:
50 = n  500
Tobey & Slater, Basic College Mathematics, 6e
4
Solving a Percent Problem: Amount Unknown
amount = percent  base
Example:
What is 9% of 65?
n
= 9%  65
n
= (0.09) (65)
n
= 5.85
5.85 is 9% of 65.
Tobey & Slater, Basic College Mathematics, 6e
5
Solving a Percent Problem: Base Unknown
amount = percent  base
Example:
36 is 6% of what?
36 = 6% 
n
36 = 0.06n
36
0.06n
=
0.06
0.06
600 = n
36 is 6% of 600.
Tobey & Slater, Basic College Mathematics, 6e
6
Solving a Percent Problem: Percent Unknown
amount = percent  base
Example:
24 is what percent of 144?
24 =
24 = 144n
24
144n
=
144
144
0.16 = n
2
16 % = n
3
n
 144
2
24 is 16 % of 144.
3
Tobey & Slater, Basic College Mathematics, 6e
7