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Algebra: Consecutive Integer 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, …
The following are common examples of consecutive integer problems.
John has a board that is 5 feet long. He plans to use it to make 4 shelves whose lengths are to be a series of consecutive even numbers. How long should each shelf be in inches?
Solution:
Step 1: Being consecutive even numbers we need to add 2 to the previous number.
The lengths of the shelves should be 12, 14, 16 and 18.
Answer: The lengths of the shelves in inches should be 12, 14, 16 and 18.
The following video shows how to solve the integer word problems:
The sum of two consecutive integers is 99. Find the value of the smaller integer.
The sum of two consecutive odd integers is 40. What are the integers?
The sum of three consecuitve even integers is 30. Find the integers.
The following video gives another example of how to solve consecutive integer word problems.
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