let

x = the present age of the teacher

y = the present age of the student

teacher is 15 years older than her student

x = y + 15

in 15 yrs the ratio of their ages will be 3:2

(x + 15) : (y + 15) = 3 : 2

by solving the system of equations

x = y + 15

(x + 15) : (y + 15) = 3 : 2

we find

x = 30 years

y = 15 years

the teacher is 30 years old and the student is 15 years old.