When numbers are in proportion to each and in reduced form, then at some point they had to have a number in common that would then reduce to 3/4.
Consider this number x. So, before it was reduced, we know that the proportion looked like this: 3x/4x and we also know that the sum is 36. Therefore, 3x + 4x =36
Thus, 7x = 36 and x = 36/7
Putting this back into the proportion of 3/4, you have 3(36/7) and 4(36/7), which means the two numbers are:
108/7 and 144/7.
This process is used quite a bit in Geometry in the study of proportional figures and angles.