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Consecutive Integer Word Problems

 

 

Consecutive integer problems are word problems that involve consecutive integers.

Consecutive integers are integers that follow in sequence, each number being 1 more than the previous number, represented by n, n +1, n + 2, n + 3, ..., where n is any integer.

For example: 23, 24, 25, …

If we start with an even number and each number in the sequence is 2 more than the previous number then we will get consecutive even integers.

For example: 16,18, 20, …

If we start with an odd number and each number in the sequence is 2 more than the previous number then we will get consecutive odd integers.

For example: 33, 35, 37, …

 

 

We will look at some examples of consecutive integer problems, consecutive odd integer problems and consecutive even integer problems.

 

Example : Consecutive Integer Problem

The sum of the least and greatest of 3 consecutive integers is 60. What are the values of the 3 integers?

Solution:

Step 1: Assign variables :

Let x = least integer

x + 1 = middle integer

x + 2 = greatest integer

Translate sentence into an equation.

Sentence: The sum of the least and greatest is 60.

Rewrite sentence:

x + (x + 2) = 60

Step 2: Solve the equation

Combine like terms

2x + 2 = 60

Isolate variable x

2x =58

equation

Step 3: Check your answer

29 + 29 + 2 = 60

The question wants all the 3 consecutive numbers: 29, 30 and 31

Answer: The 3 consecutive numbers are 29, 30 and 31.

 

 

The following video shows an example of a consecutive number word problem:

 

 

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Useful Links:
SCC - Consecutive Integer Problems
 
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