But Where's The Equation?

Relevant wiki: Setting Up Equations

Let the numbers be $x-1,x,x+1$ .Then: $\begin{aligned} (x-1)+x+(x+1)&=15+(x+1)\\ 3x &=x+16\\ \implies x&=8 \end{aligned}$ Hence $x+1=\boxed{9}$

Let the consecutive numbers be $x$ , $x+1$ and $x+2$ .

According to question,

$\Rightarrow x+x+1+x+2-15=x+2$

$3x-12=x+2$

$x=7$

Greatest number $\Rightarrow x+2=7+2=\boxed{9}$

We'll find the sum of the two smaller numbers ,which wil help in solving the problem. Since the sum of the three numbers is $15$ more than the greatest of them, then the sum of the two smaller numbers is $15$ . The numbers are consecutive, so the two smaller numbers are $7$ and $8$ . The greatest (third) number is $9$ .

Let the 3 numbers be x, x+1, x+2. By understanding the statement, we get 3x+3 = x+2+15 which will equal to 7 + 2 = 9