let one number be x

the other number will be 1200-x. ( Because the sum of both is 1200)

one number is 800 less than the 3 times the other.

The other number is 1200-x

3 times other = 3(1200-x)

less 800

= 3(1200-x) -800

x=3(1200-x)-800

x=3600-3x-800

x+3x= 2400

4x = 2400

divide by 4

x= 2400/4

x=600

if one number is 600, then other is 1200-x=600.