Beginning Algebra, 11th Edition

CHAPTER 7 Review Exercises 489

7.7 Solve each problem.

50.In a certain fraction, the denominator is 5 less than the numerator. If 5 is added to both the
numerator and the denominator, the resulting fraction is equivalent to. Find the original
fraction (notwritten in lowest terms).

51.The denominator of a certain fraction is six times the numerator. If 3 is added to the
numerator and subtracted from the denominator, the resulting fraction is equivalent to.
Find the original fraction (notwritten in lowest terms).

52.A plane flies 350 mi with the wind in the same time that it can fly 310 mi against the
wind. The plane has a speed of 165 mph in still air. Find the speed of the wind.

53.Susan Costa can plant her garden in 5 hr working alone. A friend can do the same job in
8 hr. How long would it take them if they worked together?

54.The head gardener can mow the lawns in the city park twice as fast as his assistant. Work-
ing together, they can complete the job in hr. How long would it take the head gardener
working alone?

7.8 Solve each problem.

55.Concept Check The longer the term of your subscription to Entertainment Weekly,the
less you will have to pay per year. Is this an example of direct or inverse variation?

56.If a parallelogram has a fixed area, the height
varies inversely as the base. A parallelogram has
a height of 8 cm and a base of 12 cm. Find the
height if the base is changed to 24 cm.

57.If yvaries directly as x, and x= 12 when y= 5 , find xwhen .y= 3

(^1 13)
2
5
5
4
12 cm
8 cm?
24 cm

MIXED REVIEW EXERCISES

Perform each indicated operation.

Solve.

64. 
    
    
    
    65. for v
    
    
    
    

66.Rob Fusco flew his plane 400 km with the wind in the same time it took him to go
200 km against the wind. The speed of the wind is 50 km per hr. Find the rate of the
plane in still air.

67.With spraying equipment, Lizette Foley can paint the woodwork in a small house in
8 hr. Seyed Sadati needs 14 hr to complete the same job painting by hand. If Lizette
and Seyed work together, how long will it take them to paint the woodwork?

68.If wvaries inversely as z, and when , find wwhen.

69.In a rectangle of constant area, the length and the width vary inversely. When the
length is 24, the width is 2. What is the width when the length is 12?

70.If xvaries directly as the cube of y, and x= 54 when y= 3 , find xwhen y=- 2.

w= 16 z= 3 z= 2

a=

v-w

t

2

z

z

z+ 3

=

1

z+ 3

1

t^2 - 4

+

1

2 - t

4

z^2 - 2 z+ 1

3

z^2 - 1

5

x

• 1
  5 - x
  3 x

r- 3

8

,

3 r- 9

4

8 p^5

5

,

2 p^3

10

4

m- 1

• 3
  m+ 1