SOLUTION: Can you please help me figure out what the variables for this equation would be? "The sum of two consecutive even integers is at most 400. Find the pair of integers with the greate

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Question 514005: Can you please help me figure out what the variables for this equation would be? "The sum of two consecutive even integers is at most 400. Find the pair of integers with the greatest sum." I know that theres going to be a "small" variable, and a "large" variable. I also know that the small is always going to be the 'x'. What does the 'greatest sum' even mean?
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

If you let represent the first (smaller) integer, the next consecutive even integer has to be .

Then you need to set up an inequality. The words "at most" give you a clue that you need a "less than or equal" relationship.

So .

But 199 is not even! (You complain). True enough, so you have to back down one, and the first even integer can be no larger than 198, then the next consecutive even integer is 200, and their sum is 398. If you try 200 and 202 you end up greater than 400 which the problem constraints do not allow, and if you try 196 and 198, you don't get the greatest possible sum less than 400. See?

John

My calculator said it, I believe it, that settles it