Basic Mathematics for College Students

26. Complete the following table.

Determine whether the variable is used as a factoror as a

term.See Example 2.

27. 
    
    
    
    28. 
        
    
    
    
    


28. 
    
    
    
    30. 
        
    
    
    
    

Translate each phrase to an algebraic expression. If no variable

is given, use as the variable.See Example 3.

31. The sum of the length and 15


32. The difference of a number and 10


33. The product of a number and 50


34. Three-fourths of the population


35. The ratio of the amount won and lost


36. The tax added to


37. increased by two-thirds of


38. 21 less than the total height


39. The square of , minus 2,005


40. subtracted from


41. 1 less than twice the attendance


42. reduced by 500


43. 1,000 split equal ways


44. Exceeds the cost by 25,000


45. 90 more than twice the current price


46. 64 divided by the cube of


47. 3 times the total of 35, , and 300


48. Decrease by


49. 680 fewer than the entire population


50. Triple the number of expected participants


51. The product of and 4, decreased by 15


52. The quotient of and 6, cubed


53. Twice the sum of 200 and


54. The square of the quantity 14 less than


55. The absolute value of the difference of and 2


56. The absolute value of , decreased by 2


57. One-tenth of the distance


58. Double the difference ofxand 18

d

a

a

x

t

y

d

p

x  17

h

y

p

c

n

J

a

s S

k

h

P p

t c

w l

p

l

x

5 c abc

c 32  24 c 6

c

Translate each algebraic expression into words. (Answers may

vary.)See Example 3.

59.

60.

61.

62.

63.

64.

65.

66.

Answer with an algebraic expression.See Example 4.

67. MODELING A model’s skirt is inches long. The
    designer then lets the hem down 2 inches. What is the
    length of the altered skirt?


68. PRODUCTION LINES A soft drink manufacturer
    produced cans of cola during the morning shift. Write
    an expression for how many six-packs of cola can be
    assembled from the morning shift’s production.


69. PANTS The tag on a new pair of 36-inch-long jeans
    warns that after washing, they will shrink inches in
    length. What is the length of the jeans after they are
    washed?


70. ROAD TRIPS A caravan of cars, each carrying
    5 people, traveled to the state capital for a political
    rally. How many people were in the caravan?

Evaluate each expression, for , , and.

See Example 7.

71. 
    
    
    
    72. 
        
    
    
    
    


72. 
    
    
    
    74. 
        
    
    
    
    


73. 
    
    
    
    76. 
        
    
    
    
    


74. 
    
    
    
    78. 
        
    
    
    
    


75. 
    
    
    
    80. 
        
    
    
    
    


76. 
    
    
    
    82. 
        
    
    
    
    

Evaluate each expression.See Example 7.

83. for , and


84. for , and


85. a^2  2 abb^2 for and a 5 b 1

b 3

(xa)^2 (yb)^2 x2, y1, a 5

b^2  4 ac a1, b 5 c 2



2 z^2 x

2 xy^2



2 xy^3

y 2 z

(xy)^2  0 zy 0 [(z1)(z1)]^2

(3x)y (4z)y

3 y^2  6 y 4 z^2 z 12

z 3 x y 5 x

y z

x 3 y 2 z 4

b

x

c

x

2 s 8

2 m 5

10 ab

xyz

c 19

t 50

2

3

d

3

4

r

646 Chapter 8 An Introduction to Algebra

Term 4 a  2 rc lw x

Coefficient

d

9

3

4