Ateacher has two students, one two times as old as the other. the teacher is five times as old as the older student, and in 5 years she will be five times as old as her younger student. find the teacher’s present age.

Let
 x: age of the teacher.
 y: age of the oldest student.
 z: youngest student's age
 We can solve the problem with the following system of equations:
 y = 2z
 x = 5y
 x + 5 = 5z
 Solving for x:
 z = y / 2
 y = x / 5
 Thus
 z = (x / 5) / 2
 z = x / 10
 Then,
 x + 5 = 5 (x / 10)
 x + 5 = x / 2
 (1/2) x = -5
 x = -10
 y = -2
 z = -1
 answer
 the teacher's present age is -10
 Note: the problem does not make much physical sense (but mathematically it has no problem)