Solve it in short way

Tamanola's age is $12\frac{1}{2} = \frac{25}{2}$ years.
The sum of Yamikani's and Wengani's ages is $\frac{4}{5}$ of Tamanola's age.

$$Y + W = \frac{4}{5} \times \frac{25}{2} = \frac{100}{10} = 10 \text{ years}$$

Yamikani's age is $2\frac{1}{4} = \frac{9}{4}$ years.
Subtract Yamikani's age from the sum of their ages to find Wengani's age.

$$W = 10 - \frac{9}{4}$$ $$W = \frac{40}{4} - \frac{9}{4}$$ $$W = \frac{31}{4} \text{ years}$$

$$W = 7\frac{3}{4} \text{ years}$$

Wengani's age is \boxed{\text{7\frac{3}{4} years}}.