Number Word Problems

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

2. There are two numbers whose sum is 50. Three times the first is 5 more than twice the second. 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.

8. The sum of two numbers is 41.The larger number is 1 less than twice the smaller number. Find the numbers.

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.

11. There are two numbers whose sum is 53.Three times the smaller number is equal to 19 more than the larger number. What are the numbers?

12. There are three consecutive odd integers. Three times the largest is seven times the smallest. What are the integers?

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

14. There are three consecutive integers. The sum of the first two is 35 more than the third. Find the integers.

15. A 25-foot-long board is to be cut into two parts. The longer part is 1 foot more than twice the shorter part. How long is each part?

16. Clara Nett went shopping for some canned goods which were on sale. She bought three times as many cans of tomatoes as cans of peaches and two times as many cans of tuna as cans of peaches. If Clara purchased a total of 24 cans, how many of each did she buy?

17. The first side of a triangle is 2 inches shorter than the second side. The third side is 5 inches longer than the second. If the perimeter of the triangle is 33 inches, how long is each side?

18. In the afternoon, Calvin and Hobbes rode their bicycles 4 miles more than three times the distance in miles they rode in the morning on a trip to the lake. If the entire trip was 112 miles, how far did they ride in the morning and how far in the afternoon?

19. Mr. and Mrs. Luther and their son Martin own three cars. Martin drives 10 miles per week farther with his car than her father does with his. Mr. Luther drives twice as many miles per week as Mrs. Luther. If their total mileage per week is 160 miles, how many miles per week does each drive?

20. There were 104,830 people who attended a rock festival. If there were 8110 more boys than girls, and 24,810 fewer adults over 50 years of age than there were girls, how many of each group attended the festival?

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.

25. One more than 3 times a number is the same as 5 times the number, decreased by 15. Find the number.

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

27. Ten increased by 6 times a number is the same as 4 less than 4 times the number. Find the number.

28. Eight times a number plus 3 times the number is the same as 9 more than 12 times the number. Find the number.

29. The sum of two numbers is 35. Three times the larger number is the same as 4 times the smaller number. Find the larger number.

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

30. The sum of two numbers is 24. Seven times the smaller number is the same as 5 times the larger number. Find the smaller number.

31. An orange has 20 fewer calories than a banana. If 7 bananas have the same number of calories as 9 oranges, how many calories are in a banana?

32. Keith weighs 20 kg more than Beth, while Henry weighs 30 kg less than twice as much as Beth. If Keith and Henry weigh the same, how much does Beth weigh (in kg)?

33. Cycle Paths, inc. makes bicycles, tricycles, and unicycles. Last week they made 88 more bicycles than unicycles, and 5 times as many tricycles as unicycles. If they made 40 more bicycles than tricycles, how many unicycles did they make?

34. The second of three numbers is 8 more than the first. and the third number is 3 less than 3 times the first. If the third number is 15 more than the second, find the three numbers.

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 cm² 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.