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?

teacher's age --- x

son's age ---- y

x-2 = 3y
x = 3y+2

x-7 = 2(y+2)
3y + 2 - 7 = 2y + 4
y = 9
x= 3(9)+2 = 29

thanks

yess it helped

29

So bad!

Wrong
Loser!
Just kidding. Awesome you did so well😀😀🤩🤩🤩😇

Ur right!

Thanks so much for your help!

To find the age of the math teacher, let's break down the information given.

1. "If you take two years from my present age, the result will be three times my son's age."
Let's assume the teacher's age is T, and her son's age is S. According to the information, we have the equation: T - 2 = 3S.

2. "Seven years ago, my age was twice what his will be in two years."
If we denote the teacher's age seven years ago as T-7 and their son's age in two years as S+2, we have the equation: T - 7 = 2(S + 2).

Now, we have a system of equations:
1. T - 2 = 3S
2. T - 7 = 2(S + 2)

We can solve this system of equations to find the values of T (teacher's age) and S (son's age).

From equation 1, we can rewrite it as T = 3S + 2.
Substituting this value of T in equation 2, we get: (3S + 2) - 7 = 2(S + 2).
Simplifying this equation, we have: 3S - 5 = 2S + 4.
Moving terms around, we get: S = 9.

Now that we know the son's age is 9, we can find the teacher's age using equation 1:
T = 3S + 2 = 3(9) + 2 = 27 + 2 = 29.

Therefore, the math teacher is 29 years old.

teacher's age --- x

son's age ---- y

x-2 = 3y
x = 3y+2

x-7 = 2(y+2)
3y + 2 - 7 = 2y + 4
y = 9
x= 3(9)+2 = 29