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

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

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