A teacher 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)
