272 CHAPTER 4 Systems of Linear Equations and Inequalities
OBJECTIVE 1 Solve problems about unknown numbers.
Solving a Problem about Two Unknown NumbersIn 2008, sales of sports footwear were $6627 million more than sales of sports cloth-
ing. Together, the total sales for these items amounted to $27,753 million. What were
the sales for each? (Source:National Sporting Goods Association.)
Step 1 Readthe problem. We must find 2008 sales (in millions of dollars) for
sports footwear and sports clothing. We know how much more sports
footwear sales were than sports clothing sales. Also, we know the total sales.
Step 2 Assign variables.
Let sales of sports footwear in millions of dollars,
and sales of sports clothing in millions of dollars.
Step 3 Write two equations.
Sales of sports footwear were $6627 million
more than sales of sports clothing.
Total sales were $27,753 million.Step 4 Solvethe system from Step 3. We use the substitution method, since the first
equation is already solved for x.
Second equation
Let
Combine like terms.
Subtract 6627.
Divide by 2.We substitute 10,563 for yin either equation to find that x= 17,190.
y=10,563
2 y=21,126
6627 + 2 y=27,753
16627 +y 2 +y=27,753 x= 6627 +y.
x+y=27,753
x+y= 27,753
x= 6627 + y
y=
x=
EXAMPLE 1
OBJECTIVES
Applications of Linear Systems
4.4
1 Solve problems
about unknown
numbers.
2 Solve problems
about quantities
and their costs.
3 Solve problems
about mixtures.
4 Solve problems
about distance, rate
(or speed), and time.Recall from Section 2.4the six-step method for solving applied problems. We modify
those steps slightly to allow for two variables and two equations.
Don’t stop here!Solving an Applied Problem with Two Variables
Step 1 Readthe problem carefully. What information is given? What are
you asked to find?
Step 2 Assign variablesto represent the unknown values. Use a sketch,
diagram, or table, as needed. Write down what each variable represents.
Step 3 Write two equationsusing both variables.
Step 4 Solvethe system of two equations.
Step 5 State the answer.Label it appropriately. Does it seem reasonable?Step 6 Checkthe answer in the words of the originalproblem.
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