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