There are three positive numbers. One-third of the average of all three is 8 less than the highest number. If the average of the lowest and the second-lowest number is 8, what is the highest number?

The highest number is 11.

The two smaller numbers average 8, so their sum is 16.

Let the highest be H, so the total of all three is H + 16.

One-third of the average is (H + 16)/9 and equals H - 8.

(H + 16)/9 = H - 8 gives H + 16 = 9H - 72.

8H = 88, so H = 11.