let

j = Julie's age

d = daughter's age

Carl is 45 years old which is 27 years less than twice his wife Julie's age:

2j - 27 = 45

by solving we find:

j = 36 years

click here to see the step by step solution of the equation:

Carl's daughter is 22 younger than her mother Julie:

d = j - 22

d = 36 - 22

d = 14 years

Julie is 36 years old.

Their daughter is 14 years old.