Hello, Spixol123!

In three years time Ann will one-third of her mother's age.

18 years from now, Ann will be half her mother's age.

How old is her mother now?

Let = Ann's age now.

Let = Mother's age now.

In three years, they will both be three years older.

. . Ann will be years old.

. . Mother will be years old.

At that time, Ann will be one-half her Mother's age.

. . .[1]

In eighteen years, they will both be eighteen years older.

. . Ann will be years old.

. . Mother will be years old.

At that time, Ann will be one-third her Mother's age.

. . .[2]

We have: .

Subtract [2] - [1]: .

Substitute into [2]: .

Her mother is 42 years old now.