If 3 is added to a number and the sum is tripled, the result is 21 more than the number. find the number.

If 3 is added to the number: x + 3
b) ...and the sum is tripled.. 
"The sum" is "x + 3" so: 3(x+3)
c) ...the result is 27 more than the number.
27 more than the number is x + 27 
d) Put it all together:
3(x + 3) = x + 27 
Solve for x: 
1) Distribute the left side of the equation:
3x + 9 = x + 27

2) Subtract x from each side of the equation:
2x + 9 = 27
3) Subtract 9 from each side of the equation:
2x = 18
4) Solve for x:
x = 9 
Check: 
1) x = 9
2) 3(x + 3) = x + 27
3) 3 ([9] + 3) = [9] + 27
4) 3(12) = 9 + 27
5) 36 = 36 

So, therefore The answer is correct