Find two mixed numbers so that the sum is 21 1/6 and the difference is 4 3/6

A + b = 21 1/6 --> b = 21 1/6 - a
a - b = 4 3/6

a - (21 1/6 -a) = 4 3/6
a - 21 1/6 + a = 4 3/6
2a = 21 1/6 + 4 3/6
2a = 25 4/6
2a = 154/6
a = (154/6) / 2
a = (154/6) * (1/2)
a = 154/12 
a = 12 10/12
a = 12 5/6 

b = 21 1/6 -a
b = 21 1/6 - 12 5/6
b = 20 7/6 - 12 5/6
b = 8 2/6

 
a = 12 5/6
b = 8 2/6

Double check:

a + b = 12 5/6 + 8 2/6
a + b = 20 7/6 (7/6 = 6/6 + 1/6)
a + b = 21 1/6

a - b = 12 5/6 - 8 2/6
a - b = 4 3/6