We have three numbers that we will call x, y and z.
The sum of the three is 117, so we can write:

The third number, z, is 4 times the second (y). To write this in mathematical term we do:

The first number, x, is 9 less than the second (y). Then, this is:

This is a system of linear equations with 3 unknowns and 3 equations.
We can use the two last equations to replace x and z in the first equation and find the value of y:

Now, with the value of y, we can calculate x and z:

Answer: the numbers are 12, 21 and 84.