Step 5 State the answer.The width of the rectangle is 18 cm and the length is
Step 6 Check.The length, 37 cm, is 1 cm more than cm (twice the width).
The perimeter is
as required. NOW TRY
Finding Unknown Numerical QuantitiesDuring the 2009 regular season, Justin Verlander of the Detroit Tigers and Tim Lincecum
of the San Francisco Giants were the top major league pitchers in strikeouts. The two
pitchers had a total of 530 strikeouts. Verlander had 8 more strikeouts than Lincecum.
How many strikeouts did each pitcher have? (Source:www.mlb.com)
Step 1 Readthe problem. We are asked to find the number of strikeouts each
pitcher had.
Step 2 Assign a variableto represent the number of strikeouts for one of the men.
We must also find the number of strikeouts for Justin Verlander. Since he
had 8 more strikeouts than Lincecum,
Step 3 Write an equation.The sum of the numbers of strikeouts is 530.
Lincecum’s strikeouts Verlander’s strikeouts Totals 530
Step 4 Solvethe equation.
Combine like terms.
Subtract 8.
Combine like terms.Divide by 2.s = 261
2 s
2
=
522
2
2 s = 522
2 s + 8 - 8 = 530 - 8
2 s + 8 = 530
s+ 1 s+ 82 = 530
+ 1 s+ 82 =
+ =s+ 8 =the number of strikeouts for Verlander.
Let s=the number of strikeouts for Tim Lincecum.
EXAMPLE 4
21372 + 21182 = 74 + 36 = 110 cm,
21182
21182 + 1 =37 cm.
70 CHAPTER 2 Linear Equations, Inequalities, and Applications
Tim LincecumNOW TRY
EXERCISE 3
The length of a rectangle is
2 ft more than twice the width.
The perimeter is 34 ft. Find
the length and width of the
rectangle.
NOW TRY ANSWERS
- width: 5 ft; length: 12 ft
Don’t
stop here.Step 5 State the answer.We let srepresent the number of strikeouts for Lincecum,
so Lincecum had 261. Then Verlander had
Step 6 Check.269 is 8 more than 261, and The conditions of
the problem are satisfied, and our answer checks. NOW TRY
261 + 269 = 530.
s+ 8 = 261 + 8 =269 strikeouts.
CAUTION Be sure to answer all the questions asked in the problem. InExample 4,
we were asked for the number of strikeouts for eachplayer, so there was extra work in
Step 5 in order to find Verlander’s number.
NOW TRY
EXERCISE 4
During the 2008 regular NFL
football season, Drew Brees of
the New Orleans Saints threw 4
more touchdown passes than
Kurt Warner of the Arizona
Cardinals. Together, these two
quarterbacks completed a total
of 64 touchdown passes. How
many touchdown passes did
each player complete? (Source:
http://www.nfl.com))
- Drew Brees: 34; Kurt Warner: 30