Monica, who is 18 years old, is one-third the age of her father. The age at which shewill be half the age of her father is ____

Age of Monica = 18

Age of Monica's father = 3 * 18 = 54

Let us assume that after x years, Monica's age will be half that of her father's age.

=> $$18+x=\dfrac{1}{2}\left(54+x\right)$$

=> $$36+2x=54+x$$

=> $$x=18$$

Thus, after 18 years, Monica's age will be half that of her father's age. At that time, Monica will be = 18 + 18 = 36.