The average of 5 numbers is 64. When a sixth number is added, the average becomes 66. What is the sixth number.

5 x 64 = 320

66 = (320+x) / 6

66*6 = (320 + x)

396 = 320 + x

x = 396-320 = 76

the 6th number is 76

(x+y+z+w+k) / 5 = 64, and so (x+y+z+w+k) = 5 (64) = 320.

Then, adding a sixth number, a, we get:

[ (x+y+z+w+k) + a ]/6 = 66, and (x+y+z+w+k) + a = 6 (66) = 396.

We now know that (x+y+z+w+k) + a = 6 (66) = 396, but we also know that

(x+y+z+w+k) = 320. Thus, 320 + a = 396. Then a = 76.