The average age of $24$ students in a class is $15.5$ years. The age of their teacher is $28$ years more than the average of all twenty-five. What is the age of the teacher in years?

Let the average age of all $25$ people (students + teacher) be $A$ years.According to the problem, the age of the teacher is $A+28$.The total age of the $24$ students is:
$$24\times 15.5=372\text{ years}$$
The total age of all $25$ people is the sum of the total age of the students and the age of the teacher:
$$\text{Total Age}=372+(A+28)=400+A$$
We also know that the total age is equal to $25$ times the average age $A$:
$$25A=400+A$$
$$24A=400$$
$$A=\frac{400}{24}=\frac{50}{3}=16\frac{2}{3}\text{ years}$$
The age of the teacher is:
$$\text{Teacher’s Age}=A+28=16\frac{2}{3}+28=44\frac{2}{3}\text{ years}$$