Mary's dad is 3 years less than double her age. The difference in their age is 31.

Mary is 34 years old, and Dad is 34 + 31, or 65, years old.

Step-by-step explanation:

Represent the ages of Dad and Mary by d and m respectively.

Write and solve a system of linear equations as follows:

d = 2m - 3

d - m = 31

Substituting 2m - 3 for d in the second equation, we get:

2m - 3 - m = 31

Combining like terms results in

m = 34. Mary is 34 years old, and Dad is 34 + 31, or 65, years old.