Question

The students asked their math teacher to tell them her age. she didn't want to tell them, but she replied, "if you take two years from my present age the result will be three times my son's age, and seven years ago my age was twice what his will be in two years." how old is the teacher

Answer 1

Let the teacher's age be x and son's age be y.
So of we take two years from her years the equation becomes x-2 = 3y
Then x = 3y+2 -------(1)
But 7 years ago we have
x-7 = 2(y+2) ---------(2)
Substitute value for x in (1) into (2)
3y + 2 - 7 = 2y + 4
3y - 5 = 2y + 4
y = 9; so
x= 3(9)+2 = 29.
The teacher is 29 yrs old.

Answer 2

I believe the answer is 29 years old

Let's assume that x is the teacher's age and y is the son's age.

If you take two years from my present age the result will be three times my son’s age,"
x-2 = 3y
x = 3y+2 . . . (a)

seven years ago my age was twice what his will be in two years
x-7 = 2(y+2) . . . (b)

We substitute (a in (b)
3y + 2 - 7 = 2y + 4

y = 9
x= 3(9)+2 = 29