Basic Mathematics for College Students

8.5 Using Equations to Solve Application Problems 675

66. 
    

    1 t5(t2)  10

    
    


67. 
    

    30 x 12 1,338

    
    


68. 
    

    40 y 19 1,381

    
    


69. 
    

     7  r  14

    
    


70. 
    

    21  f 19

    
    


71. 
    


72. 
    


73. 
    

    9 5(r3)  6 3(r2)

    
    


74. 
    

    2 3 (n6) 4(n 2)  21

    
    


75. 
    


76. 
    


77. 
    


78. 
    


79. 
    

    9 a2.4  7 a4.6

    
    


80. 
    

    4 c1.6  7 c3.2

    
    

4(x5)3(12x) 7

2(9 3 s)(5s2) 25



7

5

x 9  5



2

3

z 4  8

7  7 x 21

10  2 y 8

2

5

3

7

81. To solve , one student began by
    subtracting from both sides. Another student
    solved the same equation by first subtracting from
    both sides. Will the students get the same solution?
    Explain why or why not.


82. Explain the error in the following solution.
    Solve:

Name the property that is used.

83.

84. x 99  99 x


85. 
    


86. 2(30y)(230)y

(x1) 2 x(12)

x 9  9 x

REVIEW

x 11

x 4  4  15  4

x 4  15

2 x

2

 4 

30

2

2 x 4  30

5 x

3 x

3 x 4  5 x 1

WRITING

SECTION 8.5

Using Equations to Solve Application Problems

Objectives

1 Solve application problems to
find one unknown.
2 Solve application problems to
find two unknowns.
Throughout this course, we have used the steps Analyze, Form, Solve, State, and Check
as a strategy to solve application problems. Now that you have had an introduction to
algebra, we can modify that strategy and make use of your newly learned skills.

Solve application problems to find one unknown.

To become a good problem solver, you need a plan to follow, such as the following five-
step strategy. You will notice that the steps are quite similar to the strategy first introduced
in Chapter 1. However, this new approach uses the concept of variable, the translation
skills from Section 8.1, and the equation solving methods of Sections 8.3 and 8.4.

Strategy for Problem Solving

1. Analyze the problemby reading it carefully to understand the given facts.
   What information is given? What are you asked to find? What vocabulary is
   given? Often, a diagram or table will help you visualize the facts of the
   problem.


2. Form an equationby picking a variable to represent the numerical value
   to be found. Then express all other unknown quantities as expressions
   involving that variable. Key words or phrases can be helpful. Finally,
   translate the words of the problem into an equation.


3. Solve the equation.


4. State the conclusionclearly. Be sure to include the units (such as feet,
   seconds, or pounds) in your answer.


5. Check the resultusing the original wording of the problem, not the
   equation that was formed in step 2 from the words.

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