let's assume the middle number is [tex]x[/tex] then the smallest number is [tex]x-2[/tex] the greatest number is [tex]x+2[/tex] so the sum of the three number would be [tex](x-2)+x+(x+2)[/tex] and it equals 45 now we have an equation [tex](x-2)+x+(x+2)=45[/tex] then we solve it [tex]3x=45[/tex] [tex]x=15[/tex], which means the middle number equals 15 so the greatest number would be [tex]x+2=15+2=17[/tex] 17 is the greatest number
