Question 1091590

let's two consecutive even integers be {{{x}}} and {{{x+2}}}

if the sum of two {{{consecutive}}} even integers is less than {{{84}}}, we have:

{{{x+x+2<84}}}...solve for {{{x}}}

{{{2x<84-2}}}

{{{2x<82}}}

{{{x<82/2}}}

{{{x<41}}}-> the greatest even integer could be {{{40}}}

so, even integers are:{{{2}}},{{{4}}},{{{6}}},{{{8}}},{{{10}}},{{{12}}},{{{14}}},{{{16}}},{{{18}}},{{{20}}},{{{22}}},{{{24}}},{{{26}}},{{{28}}},{{{30}}},{{{32}}},{{{34}}},{{{36}}},{{{38}}},{{{40}}}

since we need two consecutive even integers,  the pair with the greatest sum will be {{{38+40=78}}}