SOLUTION: Find three consecutive odd integers such that the sum of the least integer and the greatest integer is 13 more than the middle integer.

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Find three consecutive odd integers such that the sum of the least integer and the greatest integer is 13 more than the middle integer.      Log On


   

Question 1161837: Find three consecutive odd integers such that the sum of the least integer and the greatest integer is 13 more than the middle integer.
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be the middle integer.


Then the sum of the least integer and the greatest integer is 2x, 

and the condition says


    2x - x = 13.


So, the middle integer is 13, and the three consecutive odd integers are  11, 13 and 15.

Solved.


Answer by Alan3354(69443) About Me  (Show Source):
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Three consecutive odd integers form an arithmetic sequence.

In an arithmetic sequence of three terms, the middle term is the average of the first and third -- i.e., the sum of the first and third is two times the middle term.

So if the sum of the first and third is 13 more than the middle, the middle term must be 13.

And so the three odd integers are 11, 13, and 15.

Putting the above argument in terms of formal algebra....

Let the three integers be x-2, x, and x+2

The sum of the first and third is 13 more than the middle:

%28x-2%29%2B%28x%2B2%29+=+%28x%29%2B13
2x+=+x%2B13
x+=+13

And the three integers are
x-2 = 11
x = 13
x+2 = 15