Mr. Vogt’s “Consecutive Integer Word Problems”

 

1.  Find the sum of four consecutive integers, the first of which is 21.

2.  Find the sum of three consecutive even integers beginning with –2.

3.  Find the sum of five consecutive odd integers beginning with –13.

4.  The sum of two consecutive integers is 147. Find the integers.

5.  The sum of two consecutive integers is –113. What are the integers.

6.  Find three consecutive integers whose sum is –117.

7.  Find three consecutive integers whose sum is 198.

8.  Find three consecutive even integers whose sum is 78.

9.  Find three consecutive even integers whose sum is –252.

10.  Find three consecutive odd integers whose sum is –285.

11.  Find three consecutive odd integers whose sum is 357.

12.  Find three consecutive odd integers whose sum is 126.

13.  Find four consecutive integers whose sum is 335

14.  The sum of the first two of three consecutive integers is twenty-six more than the third integer.  Find the three integers.

15.  The sum of the first and the third of three consecutive integers is thirty-two more than the second integer.  What are the three integers?

16.  Find two consecutive odd integers such that twice the first added to five times the second is 577.

17.  Find two consecutive odd integers such that four times the first less six times the second is –162.

18.  Find two consecutive odd integers such that double the first added to the second is 55 more than their sum.

19.  Find two consecutive even integers such that three times the first added to twice the second is 182 more than their sum.

20.  Find three consecutive integers such that triple the third decreased by triple the first is 15 less than the second.

21.  Find three consecutive integers such that three times the first diminished by the third is 47 more than the second.

22.  The sum of the first two of three consecutive even integers added to the sum of the last two is 232.  Find the three even integers.

23.  Find three odd consecutive integers so that three times the first diminished by the third is 47 more than the second.

24.  The sum of the first and the last of three consecutive odd integers added to the sum of the first two is -230.  Find the three odd integers.

25.  Find three consecutive even integers such that double the first added to five times the second is 78 less than the third.

26.  Find three consecutive even integers such that four times the first added to twice the second is 150 more than the third.

 

 

Answers:

1) 90       2) 0         3) -45       4) (73, 74)       5) (-57,-56)        6) (-40,-39,-38)       7) (65, 66, 67)           8) (24, 26, 28)

9) (-86, -84, -82)     10) (-97, -95, -93)    11) (117, 119, 121)     12) Æ, (40, 42, 44) are even      13) Æ       14) (27, 28, 29)

15) (31, 32, 33)    16) (81, 83)     17) (75, 77)     18) (55, 57)     19) (60, 62)       20) (20, 21, 22)      21) (50, 51, 52)

* Vogt Educational Materials

22) (56, 58, 60)          23) (53, 55, 57)                24) (-59, -57, -55)                25) (-14, -12, -10)          26) (30, 32, 34)