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

1 answer:

Ber [7]3 years ago

7 0

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!

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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 .

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