Beginning Algebra, 11th Edition

Solve each problem. See Sections 2.4 and 2.5.

83.If a number is doubled and 6 is subtracted from this result, the answer is 3684. The

unknown number is the year that Texas was admitted to the Union. What year was Texas

admitted?

84.The length of the rectangle is 3 m more than its width. The

perimeter of the rectangle is 34 m. Find the width of the rectangle.

85.Twice the sum of two consecutive integers is 28 more than the

greater integer. Find the integers.

86.The area of a triangle with base 12 in. is 48 in.^2. Find the height of the triangle.

PREVIEW EXERCISES

400 CHAPTER 6 Factoring and Applications

x+3

x

OBJECTIVES We use factoring to solve quadratic equations that arise in application problems. We

follow the same six problem-solving steps given in Section 2.4.

Applications of Quadratic Equations

6.6

1 Solve problems

involving geometric

figures.

2 Solve problems

involving

consecutive

integers.

3 Solve problems by

applying the

Pythagorean

theorem.

4 Solve problems by

using given

quadratic models.

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 unknown

values in terms of the variable.

Step 3 Write an equation,using 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 original problem.

OBJECTIVE 1 Solve problems involving geometric figures.Refer to the for-

mulas given on the inside covers of the text, if necessary.

Solving an Area Problem

Abe Biggs wants to plant a triangular flower bed in a corner of his garden. One leg

of the right-triangular flower bed will be 2 m shorter than the other leg. He wants the

bed to have an area of See FIGURE 1. Find the lengths of the legs.

Step 1 Readthe problem. We need to find the lengths of the

legs of a right triangle with area

Step 2 Assign a variable.

Let

Then x- 2 =the length of the other leg.

x=the length of one leg.

24 m^2.

24 m^2.

EXAMPLE 1

x – 2

x

FIGURE 1

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