In this lesson, we will learn how to solve algebra word problems that involve consecutive even integers.

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 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?

Solution:

Step 1: Being consecutive even numbers we need to add 2 to the previous number.

Assign variables :

Letx= 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.

Examples:

1. The sum of two consecutive integers is 99. Find the value of the smaller integer.

2. The sum of two consecutive odd integers is 40. What are the integers?

3. The sum of three consecutive even integers is 30. Find the integers.

Example: Three consecutive even integers add up to 180. Find the largest of these three integers using a linear equation. Example: The largest of five consecutive even integers is 2 less than twice the smallest. Which of the following is the largest integer?

Consecutive odd integers are set up the exact same way.

Problem: If the first and third consecutive even integers are added, the result is 22 less than 3 times the second integer. Find the integer. Consecutive Even Integer Story Problem

Problem: Find two consecutive integers such that the smaller added to four times the larger gives a sum of 28.

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