What are some examples of consecutive integers solved problems?

Solved Examples: Consecutive Integers Problems

Example 1: John has a wooden board that is 5 feet long. He plans to make 4 shelves whose lengths are to be a series of consecutive even numbers. Find the length of each shelf in inches?

Solution:

Step 1: We know that consecutive even integers are even integers that follow each other by a difference of 2.

   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: Converting feet to inches

1 feet = 12 inches

Hence, 5 × 12 = 60 inches

 Step 3: adding the 4 consecutive integers equal to 60 

x + x + 2 + x + 4 + x + 6 = 60

  Combine like terms

  4x + 12 = 60

  Isolate variable x

  4x = 60 – 12

  4x = 48

  x = 12

Step 4: substitute the values of x

  length of first shelf = x = 12 inches

  length of second shelf = x + 2 = 14 inches

  length of third shelf = x + 4 = 16 inches

  length of fourth shelf =  x + 6 = 18 inches

Therefore, the lengths of the shelves should be 12inch, 14 inch, 16 inch and 18 inch.

Let’s check our answer

12 + 12 + 2 + 12 + 4 + 12 + 6 = 60

Example 2: If the sum of three consecutive integers is 81, Find the three integers and then find what is the product of the first and the third integer?

Solution:

Step 1: Let us assume the three consecutive integers: x, x + 1 and x + 2

Step 2 : Now, as given

x + x + 1 + x + 2 = 81

3x + 3 = 81

3x = 81 – 3

3x = 78

x = 78/3

x = 26

x + 1 = 27

x + 2 = 28

Product of the first and third integer = 26 × 28 = 728.