The sum of two consecutive even integers is seventy two

Question

The sum of two consecutive even integers is seventy two

Answer 1

Assume n is an even number, such that

 

n + (n + 2) = 72

 

Then

 

2n + 2 = 72

 

2n = 72 - 2 = 70

2n = 70

n = 70/2 = 35, which is not even.  Contradiction!

 

There is no solution.  However, as noted by Andrew, the two consecutive odd integers 35 and 37 add up to 72.

Answer 2

2n + (2n+2) = 72
2n + 1(2n + 2) = 72
2n + 2n + 2 = 72
    4n + 2  =  72
         - 2  =   72 - 2 
        4n    =    70                 35
      ------  =  -----  =>  n =  ---  = 17 1/2  or 17.5  (is not an integer)
          4           4                   2