Answer:
Our three numbers are 8, 48, and 16. 
Step-by-step explanation:
Let the first, second, and third numbers be <em>x</em>, <em>y</em>, and <em>z</em>, respectively. 
The sum of them is 72. In other words: 

The second number <em>y</em> is three times the third number <em>z</em>. So: 

And the third number <em>z</em> is eight more than the first number <em>x</em>. So: 

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

Substitute again: 

Solve for <em>x</em>. 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 <em>z</em> is 16. 
The second number is three times the third. Thus, the second number <em>y</em> is 3(16) or 48. 
Our three numbers are 8, 48, and 16.