108 CHAPTER 2 Linear Equations and Inequalities in One Variable
OBJECTIVE 2 Solve problems involving unknown numbers.
OBJECTIVES
An Introduction to Applications of Linear Equations
2.4
1 Learn the six steps
for solving applied
problems.
2 Solve problems
involving unknown
numbers.
3 Solve problems
involving sums of
quantities.
4 Solve problems
involving
consecutive
integers.
5 Solve problems
involving
supplementary and
complementary
angles.OBJECTIVE 1 Learn the six steps for solving applied problems. To solve
applied problems, the following six-step method is often applicable.
NOW TRY
EXERCISE 1
If 5 is added to a number, the
result is 7 less than 3 times
the number. Find the number.
Finding the Value of an Unknown NumberIf 4 is multiplied by a number decreased by 7, the product is 100. Find the number.
Step 1 Readthe problem carefully. We are asked to find a number.
Step 2 Assign a variableto represent the unknown quantity.
Step 3 Write an equation.
Let x=the number.
EXAMPLE 1
Writing a “word equation”
is often helpful.Note the careful
use of parentheses.Step 4 Solvethe equation.
Equation from Step 3
Distributive property
Add 28.
Combine like terms.Divide by 4.Step 5 State the answer.The number is 32.
Step 6 Check.When 32 is decreased by 7, we get If 4 is multiplied
by 25, we get 100, as required. The answer, 32, is correct. NOW TRY
32 - 7 = 25.
x= 32
4 x
4
=
128
4
4 x= 128
4 x- 28 + 28 = 100 + 28
4 x- 28 = 100
41 x- 72 = 100
NOW TRY ANSWER
- 6
If 4 is multiplied a decreased the product
by number by 7, is 100.4 # 1 x - 72 = 100
Solving an Applied Problem
Step 1 Readthe problem carefully. What information is given? What are
you asked to find?
Step 2 Assign a variableto represent the unknown value. Use a sketch,
diagram, or table, as needed. If necessary, express any other un-
known values in terms of the variable.
Step 3 Write an equationusing the variable expression(s).
Step 4 Solvethe equation.
Step 5 State the answer.Label it appropriately. Does it seem reasonable?
Step 6 Checkthe answer in the words of the originalproblem.http://www.ebook777.com
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