Beginning Algebra, 11th Edition

SECTION 4.4 Applications of Linear Systems^277

5.According to Natural Historymagazine, the speed of a cheetah is 70 mph. If a cheetah

runs for xhours, how many miles does the cheetah cover?

A. B. C. miles D. 70 xmiles

6.How far does a car travel in 2.5 hr if it travels at an average rate of xmiles per hour?

A. miles B. miles C. miles D. 2.5xmiles

7.What is the speed of a plane that travels at a rate of 650 mph witha wind of rmph?

A. mph B. C. D.

8.What is the speed of a plane that travels at a rate of 650 mph againsta wind of rmph?

A. B. mph C. D.

Exercises 9 and 10 are good warm-up problems. Refer to the six-step problem-solving method,

fill in the blanks for Steps 2 and 3, and complete the solution by applying Steps 4 – 6.

9.The sum of two numbers is 98. The difference between them is 48. Find the two numbers.

Step 1 Readthe problem carefully.

Step 2 Assign variables.

Let the first number and let.

Step 3 Write two equations.

First equation: ; Second equation:

10.The sum of two numbers is 201. The difference between them is 11. Find the two numbers.

Step 1 Readthe problem carefully.

Step 2 Assign variables.

Let the first number and let.

Step 3 Write two equations.

First equation: ; Second equation:

Write a system of equations for each problem, and then solve the system. See Example 1.

x+y= 201

x= y=

x+y= 98

x= y=

1650 - r 2 mph 1 r- 6502 mph

650

r

1650 +r 2 mph

1650 - r 2 mph 1650 +r 2 mph 1 r- 6502 mph

r

650

x

2.5

2.5

x

1 x+2.5 2

70

x

170 +x 2 miles 170 - x 2 miles

11.The two longest-running shows in

Broadway history were The Phantom of

the Operaand Cats. As of October 7,

2008, there had been a total of 16,088

performances of the two shows, with

1118 more performances of The Phan-

tom of the Operathan Cats. How many

performances were there of each show?

(Source:The Broadway League.)

12.Two other musicals that had long Broad-

way runs were A Chorus Line and

Beauty and the Beast. There were 676

fewer performances of Beauty and the

Beastthan of A Chorus Line,and a total

of 11,598 performances of the two

shows. How many performances were

there of each show? (Source: The

Broadway League.)