Final answer:
Using algebra, we found out that Linda, who is currently 12 years old, will be one-third her father's age in 3 years. Linda's father is 42 years old at the moment, and Linda is 2/7 of his age.
Step-by-step explanation:
Linda is (2/7) her father's age currently. Since her father will be 47 years old in 5 years, his current age is 47 - 5 = 42 years old. That means Linda is currently (2/7) × 42 = 12 years old.
To find out when Linda will be (1/3) her father's age, let's denote Linda's age as L and her father's age as F. We know that L = (2/7)F and in 5 years F will be 47, so right now F = 42. If x is the number of years until Linda is (1/3) her father's age, the equation would be L + x = (1/3)(F + x). By substituting the known values, we get 12 + x = (1/3)(42 + x).
Multiplying both sides by 3 to clear the fraction gives us 36 + 3x = 42 + x. Simplifying, we get 2x = 6, hence x = 3. So, in 3 years, Linda will be one-third her father's age.