Discussion of Question with ID = 022 under Averages

Each of the 5 items of a sample has a value 78 units. If a new item with a value 55 units more than the average of all 6 items is added, what is the sum total of the values of all 6 items?

Let the average of all 6 items be x, then the required total is T = 6x. By averages, $x = {5 × 78 + (x + 55)}/6$ which is same as $x × 6 = {5 × 78 + (x + 55)}$, which is same as $T = {5 × 78 + (T/6 + 55)}$, solving for T we get 534 units.