Question

Two numbers differ by 9. the large number is 20 greater than half of the smaller number. find the two numbers

Answer 1

Using x to represent the larger number and y to represent the smaller number, do this:
x - y = 9
x = 1/2y + 20
(1/2y + 20) - y = 9
(1/2y - y) + 20 = 9
-1/2y + 20 = 9
         -  20  - 20
-1/2y = -11
Divide each side by -1/2 to find y
y = 22
Plug the y value into the first equation
x - 22 = 9
  + 22 + 22
x = 31

The larger number is 31 and the smaller number is 22

Answer 2

Large = 20+ 1/2 of small and,

Large-small =9 so if we put back the 9 to the small one will get the large number
Large=9+small

Now we can see that
20+small/2 =9+ small
20-9=small-small/2
11=half of small so small is 22

Large = 20 + 11=31