SOLUTION: Solving Problems involving Inequalities The sum of two consecutive even integers is at most 180. Find the pair of integers with the greatest sum.

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Question 664172: Solving Problems involving Inequalities
The sum of two consecutive even integers is at most 180. Find the pair of integers with the greatest sum.
Found 2 solutions by pv=nrt15rcks, MathTherapy:
Answer by pv=nrt15rcks(23) About Me  (Show Source):
You can put this solution on YOUR website!
What are the largest 2 whole numbers that are consecutive (i.e.1,2; 56,57) that can add up to 180? The largest I got was 89 and 90. Think about why.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Solving Problems involving Inequalities
The sum of two consecutive even integers is at most 180. Find the pair of integers with the greatest sum.

Let the smaller of the two integers be S

Then larger = S + 2

We now have: S+%2B+S+%2B+2+%3C=+180

2S+%2B+2+%3C=+180

2S+%3C+=+180+-+2

2S+%3C=+178

S+%3C=+178%2F2, or S+%3C=+89

Now, since S+%3C=+89, S CANNOT be 89 since we're looking for two EVEN integers. Therefore, the largest EVEN integer < 89 is 88, which makes the larger EVEN integer, 90.

Pair of EVEN integers with greatest sum = highlight_green%2888_and_90%29, which results in a sum of 178.

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