Question

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.

Answer 1

Let's call the younger student's age A and the older student's age B. The teacher's age will be T.

B = 2A
T = 5B
T+5 = 5(A+5)

Simplify the last equation.

T+5 = 5A+25
T = 5A+20

Now we have two equations solved for T, so we can set them equal to each other.

5B = 5A + 20

We can plug 2A in for B

5(2A) = 5A + 20

10A = 5A + 20

5A = 20

A = 4

To find T, we plug 4 in for A in T = 5A + 20

T = 5(4) + 20

T = 40

The answer is 40 years old.