The sum of four consecutive integers is 104. Find the integers.

Question

 How is it solved? 

Answer 1

You may choose any of the four consecutive integers to be x.  We will use the least one.

 

Let  x  (x+1)   (x+2)   (x+3)    be the four consecutive integers.

 

Their sum:

   x  + (x+1) + (x+2) + (x+3)  =  104

    4x + 6 = 104                    [collect like terms]

     4x = 98                [subtract 6 from both sides]

      x  = 27                [divide both sides by 4]

      x= 24.5   [rats!  that's not an integer !]

 

What does that mean -- Well, there are not four consecutive integers whose sum is 104.

Here are some close ones:

     24+ 25 + 26 + 27 = 102

     25 + 26 + 27 + 28  =  106

 

Some additional activity:  (1) could they be 'consecutive odd integers?'  (2) could they be 'consecutive even integers?'

Answer 2

We start by letting x represent the smallest number. The next three consecutive integers would each be represented by (x+1), (x+2), and (x+3). If these four numbers have a sum of 104, then we can solve for x:

 

(x) + (x+1) + (x+2) + (x+3) = 104

4x + 6 = 104

4x = 98

x=24.5

 

This answer is not an integer like the question is asking for, but it is the correct value for x based on the given number 104. If the problem specifically mentioned consecutive odd integers or consecutive even integers, we could set up the numbers as (x), (x+2), (x+4), and (x+6):

 

(x) + (x+2) + (x+4) + (x+6) = 104

4x + 12 = 104

4x = 92

x = 23.

 

In this scenario, the consecutive ODD integers would be 

    x = 23

x+2 = 25

x+4 = 27

x+6 = 29