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
