Question

The sum of the least and greatest of three consecutive integers is 72 . what are three integers?

Answer 1

If the integers are consecutive, then each one is 1 more than the one before it.

Three consecutive integers are  x,  x+1,  and  x+2 .

The sum of the least and the greatest is  (x   +   x+2)  =  2x + 2 .

You have said that this sum is 72.  So      2x + 2 =  72

Subtract  2  from each side:                      3x       =  70
Divide each side by  2 :                              x        =  35 .

The smallest is 'x'     =     35
The next one is x+1 =      36
The next one is x+2 =      37 .

Check:
The sum of the least and greatest is (35 + 37) = 72.    yay!

==================================

A slightly slicker, more fun way to do this:

Three consecutive integers.
Call the middle one 'x'.
Then the smallest one is (x-1), and the biggest one is (x+1).

The sum of the smallest and the largest one is  72 .

           (x-1) + (x+1) = 72

                     2x        = 72

                       x        = 36

           (x-1) = 35
              x    = 36
           (x+1) = 37 .