Let's assume the smaller number is x.
According to the given information, the larger number is 39 greater than the smaller number, so the larger number is x + 39.
If we add 9 to the larger number, it will be 3 times greater than the smaller number. In equation form, this can be written as:
x + 39 + 9 = 3x
Simplifying the equation, we have:
x + 48 = 3x
Subtracting x from both sides, we get:
48 = 2x
Dividing both sides by 2, we have:
24 = x
The larger number is x + 39, so substituting the value of x, we get:
x + 39 = 24 + 39 = 63
Therefore, the larger number is 63.