Consecutive integer problems are word problems that involve consecutive integers.What are 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, …What are consecutive even integers?
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, …What are consecutive odd integers?
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 now look at some examples of consecutive even integer problems.
How to solve Consecutive Even Integer Word Problems?
Example : Consecutive Even Integer
John has a board that is 3 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?
Step 1: Being consecutive even numbers we need to add 2 to the previous number.
Assign variables :
Let x = length of first shelf
x + 2 = length of second shelf
x + 4 = length of third shelf
x + 6 = length of fourth shelf
Step 2: Convert 3 feet to inches
3 × 12 = 36
Step 3: Sum of the 4 shelves is 36
x + x + 2 + x + 4 + x + 6 = 36
Combine like terms
4x + 12 = 36
Isolate variable x
4x = 36 – 12
4x = 24
x = 6
Step 3: Check your answer
6 + 6 + 2 + 6 + 4 + 6 + 6 = 36
The lengths of the shelves should be 6, 8, 10 and 12.
Answer: The lengths of the shelves in inches should be 6, 8, 10 and 12.