Fundamentals of Mathematics, 2008a

662 CHAPTER 11. ALGEBRAIC EXPRESSIONS AND EQUATIONS
11.6.3.1 Exercises for Review
Exercise 11.6.52 (Solution on p. 688.)
(Section 4.7) 8 9 of what number is 2 3 ?
Exercise 11.6.53
(Section 5.3) Find the value of 21
40 + 17
30 .
Exercise 11.6.54 (Solution on p. 688.)
(Section 5.4) Find the value of 3 1
12 + 4 1 3 + 1 1 4 .
Exercise 11.6.55
(Section 6.3) Convert 6.11 1 5
to a fraction.
Exercise 11.6.56 (Solution on p. 688.)
(Section 11.5) Solve the equation 3x 4 + 1 = −5.
11.7 Applications II: Solving Problems 7
11.7.1 Section Overview
• The Five-Step Method
• Number Problems
• Geometry Problems
11.7.2 The Five Step Method
We are now in a position to solve some applied problems using algebraic methods. The problems we shall
solve are intended as logic developers. Although they may not seem to reect real situations, they do serve
as a basis for solving more complex, real situation, applied problems. To solve problems algebraically, we
will use the ve-step method.
Strategy for Reading Word Problems
When solving mathematical word problems, you may wish to apply the following "reading strategy."
Read the problem quickly to get a feel for the situation. Do not pay close attention to details. At the rst
reading, too much attention to details may be overwhelming and lead to confusion and discouragement.
After the rst, brief reading, read the problem carefully in phrases. Reading phrases introduces information
more slowly and allows us to absorb and put together important information. We can look for the unknown
quantity by reading one phrase at a time.
Five-Step Method for Solving Word Problems
1. Let x (or some other letter) represent the unknown quantity.
2. Translate the words to mathematical symbols and form an equation. Draw a picture if possible.
3. Solve the equation.
4. Check the solution by substituting the result into the original statement, not equation, of the problem.
5. Write a conclusion.
If it has been your experience that word problems are dicult, then follow the ve-step method carefully.
Most people have trouble with word problems for two reasons:
1. They are not able to translate the words to mathematical symbols. (See Section 11.5.)
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