Write SQL query to solve given problem: What is the average number of root beers of the brand A&W sold in a day in August, 2014?. Keep the solution inside sql tag ```sql [SQL-Query] ```
SELECT CAST(COUNT(T1.BrandID) AS REAL) / 31 FROM rootbeer AS T1 INNER JOIN `transaction` AS T2 ON T1.RootBeerID = T2.RootBeerID INNER JOIN rootbeerbrand AS T3 ON T1.BrandID = T3.BrandID WHERE T2.TransactionDate LIKE '2014-08%' AND T3.BrandName = 'A&W'