Answer:
Our three numbers are 8, 48, and 16.
Explanation:
Let the first, second, and third numbers be x, y, and z, respectively.
The sum of them is 72. In other words:

The second number y is three times the third number z. So:

And the third number z is eight more than the first number x. So:

To find the numbers, solve for the system. We can substitute the last two equations into the first:

Substitute again:

Solve for x. Distribute:

Combine like term:

Subtract:

And divide:

Thus, the first number is eight.
And since the third number is eight more than the first, the third number z is 16.
The second number is three times the third. Thus, the second number y is 3(16) or 48.
Our three numbers are 8, 48, and 16.