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

Answer: 40 years old

Explanation:

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.

Answer 2

Let x = the older student
Let y = the younger student
Let z = the teacher.

x = 2y
z = 5x
z + 5 = 5y Somehow this does not look like its going to be nice.
z = 5y - 5
Since z = 5y - 5 we have
5y - 5 = 5x
y - 1 = x Here's the problem. there is a contradiction. You need to make y bigger, not smaller.