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.


Let the smaller of the two integers be S


Then larger = S + 2


We now have: {{{S + S + 2 <= 180}}}


{{{2S + 2 <= 180}}}


{{{2S < = 180 - 2}}}


{{{2S <= 178}}}


{{{S <= 178/2}}}, or {{{S <= 89}}}


Now, since {{{S <= 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(88_and_90)}}}, which results in a sum of 178.


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