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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation
2.13 Word Problems - Basic Operations With Variables - Consecutive Integers

Consecutive integers are integers that follow one another:
Example:
1,2,3........
34,35,36.......
-9,-8, -7,........
Let x represent an integer, x+1 represents the next consecutive integer, x+2 the integer after that and so on......

Consecutive even integers are even integers that follow one another. We have to add 2 to the preceding even integer to get to the next consecutive even integer:
Example: 6,8,10........
342, 344, 346......
-12,-10,-8......
If x represents the first even integer
x+2 represents the second even integer
x+4 represents the third even integer and so on........
x, x+2, x+4...............

Consecutive odd integers are odd integers that follow one another. Just as even integers we have to add 2 to the preceding odd integer to get to the next consecutive odd integer:
Example: 5,7,9........
341, 343, 345......
-11,-9,-7......
If x represents the first odd integer
x+2 represents the second odd integer
x+4 represents the third odd integer and so on........
x, x+2, x+4...............

Example:
Find two consecutive integers whose sum is 155.
Let x = the first integer
Let x + 1 = the second integer
the sum of two integers is 155
x + x + 1 = 155
2x + 1 = 155
2x = 154
x = 77
x+1 = 77+1 = 78
Answer: The two consecutive integers whose sum is 155 are 77 and 78.

Example:
Determine three consecutive integers such that twice the sum of the first and second is 27 more than three times the third.
Let x = the first integer
Let x+1 = the second integer
Let x + 2 = the third integer
twice the sum of the first and second is 27 more than three times the third:
2(x + x+1) = 3(x+2)+ 27
2(2x+1) = 3x + 6 + 27
4x + 2 = 3x + 6 + 27
4x - 3x = 6 + 27 - 2
x = 33 - 2
x = 31
x+1 = 32
x+2 = 33
Answer: The three consecutive integers are 31, 32, 33

Example:
Find the consecutive positive even integers whose sum is 94.
Let x = the first even integer
Let x + 2 = second even integer
sum of the integers is 94: x + x+2 = 94
2x + 2 = 94
2x = 92
x = 46
x+2 = 48

Example:
The sum of two consecutive integers is 25. Find the two numbers. Let n be the first integer
Then n + 1 is the second even integer
sum of the integers is 25 implies that n + (n + 1) = 25
n + (n + 1) = 25
2n + 1 = 25
2n = 24
n = 12
n + 1 = 13
The two numbers are 12 and 13

Example:
The product of two consecutive negative even integers is 24. Find the numbers.
Let n be the first integer
then n + 2 is the second integer
n(n+2) = 24
n2 + 2n = 24
n2 + 2n - 24 = 0
(n+6)(n-4)= 0
n = -6 and n = 4
The solutions are n = -6 and n = 4. Since the number we are looking for is a negative the solution is n = -6
n = -6
n + 2 = -6 + 2 = -4
Therefore the two numbers are -6 and -4

Directions: Solve the following equations with three variables.
Q 1: Find the three consecutive integers such that three times the largest is 9 less than four times the smallest. (Hint: Let three consecutive integers be x, x+1, x+2. three times the largest is 9 less than four times the smallest: 3(x+2) = 4x-9 x=?, x+1=?, x+2=?
11,12,13
21,22,23
15,16,17

Q 2: Find three consecutive integers whose sum is 54.
12,13,14
17, 18, 19
16,17,18

Q 3: Find the consecutive odd integers whose sum is 117.
37, 39. 41
23,25,27
27,29,31

Q 4: Four consecutive integers add up to 98. Find the integers.
19, 20, 21, 22
23, 24, 25, 26
25, 26, 27, 28

Q 5: Find the consecutive even integers whose sum is 132.
42,44,46
24,26,28
36,38,40

Q 6: If three consecutive integers add up to 225, what are they?
74, 75, 76
66, 67, 68
71, 72, 73

Q 7: What are three consecutive integers such that three times the smallest added to 7 is 13 less than four times the largest? (Hint: Let three consecutive integers be x, x+1, x+2. three times the smallest added to 7 is 13 less than four times the largest: 3x+7 = 4(x+2)-14 then x=?, x+1=?, x+2=?
8,9,10
12,13,14
15,16,17

Q 8: Determine two consecutive integers whose sum is 223.
101, 102
111, 112
112,113

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Question 10: This question is available to subscribers only!


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