1.A student is 6 times younger than her teacher.Three years ago the product of their ages was 36.Find their present ages .

Answer 1

".A student is 6 times younger than her teacher"
--> usually stated as,
teacher is 6 times older than the student

age of student --- x
age of teacher ---- 6x

3 years ago:
student : x-3
teacher : 6x-3

(x-3)(6x-3) = 36
6x^2 - 21x + 9 - 36 = 0
6x^2 - 21x - 27 = 0
2x^2 - 7x - 9 = 0
(2x - 9)(x + 1) = 0
x = 4.5 or x = -1, reject the negative age

The present age of the student is 4.5 years
the age of the teacher is 27

check:
3 years ago:
student was 1.5
teacher was 24
product = 1.5(24) = 36
My answer is correct