A sketch is helpful here. See FIGURE 2.
112 CHAPTER 2 Linear Equations and Inequalities in One Variable
2 x xx – 10
FIGURE 2Step 3 Write an equation.
middle- total
Longest plus sized plus shortest is length.2 xx 70
Step 4 Solve. Combine like terms.
Add 10.
Combine like terms.Divide by 4.Step 5 State the answer.The middle-sized piece is 20 in. long, the longest piece is
long, and the shortest piece is in. long.
Step 6 Check.The lengths sum to 70 in. All problem conditions are satisfied.
NOW TRYOBJECTIVE 4 Solve problems involving consecutive integers.Two integers
that differ by 1 are called consecutive integers.For example, 3 and 4, 6 and 7, and
and are pairs of consecutive integers. See FIGURE 3.
In general, if x represents an integer, represents the next greater
consecutive integer.
Finding Consecutive IntegersTwo pages that face each other in this book have 225 as the sum of their page num-
bers. What are the page numbers?
Step 1 Read the problem. Because the two pages
face each other, they must have page numbers
that are consecutive integers.
Step 2 Assign a variable.
Let
Then
Step 3 Write an equation.The sum of the page numbers is 225.
Step 4 Solve. Combine like terms.
Subtract 1.x= 112 Divide by 2.
2 x= 224
2 x+ 1 = 225
x+ 1 x+ 12 = 225
x+ 1 = the greater page number.
x=the lesser page number.
EXAMPLE 6
x 1
- 2 - 1
21202 = 40 in. 20 - 10 = 10
x= 20
4 x
4
=
80
4
4 x= 80
4 x- 10 + 10 = 70 + 10
4 x- 10 = 70
+ + 1 x- 102 =
0 15xx 1
234
1 unitConsecutive integersFIGURE 3x
x + 1NOW TRY ANSWER
- practicing free throws: 1 hr;
lifting weights: 2 hr;
watching game films: 3 hr
NOW TRY
EXERCISE 5
A basketball player spent 6 hr
watching game films, practic-
ing free throws, and lifting
weights. He spent twice as
much time lifting weights as
practicing free throws and
2 hr longer watching game
films than practicing free
throws. How many hours did
he spend on each task?
http://www.ebook777.com
http://www.ebook777.com