math age problem

Question

One day in math class, Shelly asked the teacher: "Mr. Nelson, how old are you?" Mr.Nelson responded: " This year I am three times as old as my sister. However, six years ago, I was five times as old as she was". How old is the teacher?

Answer 1

Sister is x

He is 3x

6 years ago:

Sister was (x-6)

He was 5(x-6)

6 years ago + 6 years = his current age

5(x-6) + 6 = 3x

5x - 30 + 6 = 3x

5x - 24 = 3x

2x - 24 = 0

2x = 24

x = 12

She is 12.

He is 36.

6 years ago, she was 6 and he was 30 which is 5 times as old.