In a farm there are goats and geese. They have a total of 35 heads and 100 legs. How many goats and geese are there?

Let the number of goats be ( g ) and the number of geese be ( e ). We can set up the equations: ( g + e = 35 ) (for heads) and ( 4g + 2e = 100 ) (for legs). Solving these simultaneously, we find ( g = 15 ) and ( e = 20 ). Therefore, there are 15 goats and 20 geese on the farm.