The sum of two consecutive even integers is at most 400. How do you find the pair of integers with the greatest sum?

Nov 23, 2016

198 and 200

Explanation:

Let the two integers be 2n and 2n+2
The sum of these is 4n +2
If this is cannot be more than 400
Then $4 n + 2 \le 400$
$4 n \le 398$
$n \le 99.5$
As n is a whole number the greatest n can be is 99
The two consecutive even numbers are 2x99, 198 and 200.

Or more simply say half of 400 is 200 so that is the larger of the two consecutive even numbers and the other is the one before , 198.