Currently, I am $9$ times as old as my son. Next year, I will be $7$ times as old as my son. How old is my son now?

He is 3 years old.

Step-by-step explanation:

3 times 9 is 27. She is 9 times older than her 3 year old son.

Next year he will be 4 and she will be 28. 4 times 7 is 28. She will be 7 times older than her son.

The son is 3 years now.

Step-by-step explanation:

Let x and y represent his age and his son's age respectively.

Given;

I am $9$ times as old as my son

9y = x 1

Next year, I will be $7$ times as old as my son.

7(y+1) = x + 1 2

Substituting equation 1 to 2;

7(y+1) = 9y + 1

7y + 7 = 9y + 1

Collecting the like terms

9y - 7y = 7 -1

2y = 6

y = 6/2 = 3

Since x = 9y

x = 9(3)

x = 27

The son is 3 years and he is 27 years now.