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.