Question 13239
Hi. Let x = an even integer.  Let's first examine an equation equal to 250.  We have, x + (x+2) + (x+4) + (x+6) = 250.  So x+x+2+x+4+x+6=260.  Adding like terms, we have 4x+12=250.  Solving this equation for x: 4x+12-12=250-12 leads to 4x=238.  Now, dividing by 4 on both sides yields x=59.5.  Now when x = 60 the sum of these for consecutive even integers will be greater than 250. So, the first even integer "down" from 59.5 is 58.  We have 58 + 60 + 62 + 64 = 244.  The greatest possible value for one of these integers is 64.