**
**

**Respect Responsibility
Readiness**

1.
There are two numbers whose
sum is 72. One number is twice the other. What are the numbers?

3.
Separate 71 into two parts
such that one part exceeds the other by 7. What are the numbers?

4.
Find three consecutive
integers whose sum is 87.

5. Find three consecutive even integers such that the largest is three times the smallest.

6. Four consecutive odd integers have a sum of 64. Find the integers.

7.
There is a number such that
three times the number minus 6 is equal to 45. Find the number.

9.
Separate 90 into two parts
so that one part is four times the other part.

10. The sum of three consecutive integers is 54. Find the integers.

13.
The sum of four consecutive
even integers is 44. What are the numbers?

22. Seven times a number is the same as 12 more
than 3 times the number. Find the number.

23. Six more than 5 times a number is the same as
9 less than twice the number. Find the number.

24. Three less than 11 times a number is the same
as the number decreased by 13. Find the number.

26. Twelve less than a number is the same as 6,
decreased by 8 times the number. Find the number.

(HINT: Let x = larger number and 35 - x = smaller
number.)

35. In the championship game, Julius scored 5
points less than Kareem, and Wilt scored 1 point more than twice as many as
Kareem. If Wilt scored 20 points more than Julius, how many points were scored
by each player?

36. Model Cars, Inc. makes red cars. white cars,
and blue cars. The profit on a blue car is $10 more than the profit on a white
car, and the profit on a red car is $7 less than the profit on a white car. If
the profit on two red cars is $2 less than the profit on one blue car, what is
the profit on a blue car?

37. Last year Greg’s mother weighed 3 times as
much as Greg. Since then Greg has gained 9 kg and his mother has lost 4 kg. Now
his mother weighs only twice as much as Greg. Find their weights now.

38. A hamburger costs 30 cents more than a hot
dog and 20 cents less than a cheeseburger. If 3 hamburgers cost 75 cents less
than 2 hot dogs and 2 cheeseburgers, how much does a hamburger cost?

39. Smedly has just drawn two rectangles. The
length of the first rectangle is 4 cm more than the length of the second. The
width of the first is 9 cm; the width of the second is 6 cm. If the area of the
first rectangle is 96 cm^{2 }greater than the area of the second, find
the length of each.

40. The second of two numbers is 7 times the
first. Their sum is 72. Find the numbers.

41. The larger of two numbers is 5 less than
twice the smaller. Their sum is 43. Find the numbers.

42. The sum of two numbers is 75. The first is 9
more than 5 times the second. Find the first number.

43. Jack’s bowling score is 20 less than 3
times Jill’s score. The sum of their scores is 220. Find the score of each.

44. Jennifer cut a board 2 m long into two
pieces. One piece is 24 cm shorter than the other. Find the length of each
piece.

45. With optional equipment, an automobile cost
$9120. If the cost of the basic car was $120 more than 4 times the price of the
optional equipment, what was the cost of the basic car?

46. The sum of three numbers is 207. The second
number is 8 times the first, while the third is 3 less than the first. Find the
numbers.

47. The sum of three numbers is 161. The second
number is 6 times the first, and the third is 5 more than the second. Find the
numbers.

48. A group of backpackers hiked 38 km over three
days. The first day, they hiked 1 km less than 3 times as far as the second day.
The third day, they hiked 2 km less than the first day. How far did they hike
the first day?

49. One week, Huey worked 7 hours less than Dewey, and Louie worked twice as long as Huey. Together they worked 87 hours. Find the number of hours worked by each.

50. The sum of two numbers is 90. Their
difference is 18. Find the numbers.

51. The second of two numbers is 4 more than the
first. The sum of the numbers is 56. Find the numbers.

52. The number of girls at Sky High School is 60
greater than the number of boys. If there are 1250 students all together, how
many girls are there?

53. The second of two numbers is 5 more than
twice the first. The sum of the numbers is 44. Find the numbers.

54. The sum of two numbers is 75. The second
number is 3 less than twice the first. Find the numbers.

55. The larger of two numbers is 8 more than four
times the smaller. If the larger is increased by four times the smaller, the
result is 40. Find the numbers.

56. The number of calories in a piece of pie is
20 less than three times the number of calories in a scoop of ice cream. The pie
and ice cream together have 500 calories. How many calories are in each?

57. The sum of two numbers is 4 less than twice
the larger. If the larger is decreased by three times the smaller, the result is
-20. Find the numbers.

58. Three times the larger of two numbers is
equal to four times the smaller. The sum of the numbers is 21. Find the numbers.

59. The difference between two numbers is 16.
Five times the smaller is the same as 8 less than twice the larger. Find the
numbers.

60. The larger of two numbers is 1 more than
twice the smaller. The sum of the numbers is 20 less than three times the
larger. Find the numbers.

61. Two records and three tapes cost $31. Three
records and two tapes cost $29. Find the cost of each record and each tape.

62. The sum of two numbers is the same as four
times the smaller number. If twice the larger is decreased by the smaller, the
result is 30. Find the numbers.

63. A group of students go out for lunch. If two
have hamburgers and five have hot dogs, the bill will be $8.00. If five have
hamburgers and two have hot dogs, the bill will be $9.50. What is the price of a
hamburger?

64. The price of a sweater is $5 less than twice
the price of a shirt. If four sweaters and three shirts cost $200, find the
price of each shirt and each sweater.

65. A shipment of TV sets, some weighing 30 kg
each and the others weighing 50 kg each, has a total weight of 880 kg. If there
are 20 TV sets all together, how many weigh 50 kg?

66. The second of two numbers is 4 times the first. Their sum is 50. Find the numbers.

67. The larger of two numbers is 12 more than the smaller. Their sum is 84. Find the numbers.

68. The sum of two numbers is 45. The first is 9 less than the second. Find the numbers.

69. The second of two numbers is 5 more than twice the first. Their sum is 80. Find the numbers.

70. The larger of two numbers is 1 less than 3 times the smaller. Their sum is 63. Find the numbers.

71. Find two numbers whose sum is 92, if the first is 4 more than 7 times the second.

72. The sum of two numbers
is 172. The first is 8 less than 5 times the second. Find the *first *
number.

73. Together, a necklace and a bracelet cost $192. Find the price of each if the necklace costs 3 times as much as the bracelet.

74. Grandpa’s age is 6 years less than 6 times Junior’s age. The sum of their ages is 78. Find each of their ages.

75. The first of two films
lasted 3 minutes less than twice as long as the second. Together the two films
lasted 132 minutes. How long was the *first *film?

76. The second of two numbers is 6 times the first. Their sum is 77. Find the numbers.

77. The second of two numbers is 3 less than twice the first. Their sum is 36. Find the numbers.

78. The sum of two numbers is 84. The first is 9 more than 4 times the second. Find the first number.

79. The larger of two numbers is 1 less than 8 times the smaller. Their sum is 179. Find the numbers.

80. An 84-meter length of cable is cut so that one piece is 18 meters longer than the other. Find the length of each piece.

81. A bottle filled with water weighs 9.6 kilograms. If the water by itself weighs 5 times as much as the bottle, what is the weight of the bottle?

82. Andy’s weight is 5 kilograms less than twice his brother’s. Together they weigh 100 kilograms. What are their weights?

83. The sum of three numbers is 61. The second number is 5 times the first, while the third is 2 less than the first. Find the numbers.

84. The sum of three numbers is 84. The second number is twice the first, and the third is 4 more than the second. Find the numbers.

85. Together a chair, a table, and a lamp cost $562. The chair costs 4 times as much as the lamp, and the table costs $23 less than the chair. Find the cost of the table.

86. The sum of the angle measures of any triangle is 180°. Find the angle measures of a triangle if the second angle measures 100 less than twice the first, and the third angle measures 25° more than the second.