A + 9 a+ 31 ——- = ——— 9 27

To solve the equation

\[ \frac{a + 9}{9} = \frac{a + 31}{27}, \]

we can start by cross-multiplying:

\[ 27(a + 9) = 9(a + 31). \]

Now, let's expand both sides:

\[ 27a + 243 = 9a + 279. \]

Next, we can move all terms involving \(a\) to one side and constant terms to the other side:

\[ 27a - 9a = 279 - 243. \]

This simplifies to:

\[ 18a = 36. \]

Now, divide both sides by 18:

\[ a = 2. \]

So, the solution is

\[ \boxed{2}. \]