Afarmhouse shelters 11 animals. some are goats and some are ducks. altogether there are 34 legs. how many of each animal are there?

We are given that there are 11 animals with a total of 34 legs.

 Let G = number of Goats, and D = number of Ducks

 then G + D = 11; solving for G, we get G = 11 - D

 then, 4G + 2D = 34

 substituting the value for G, we get 4(11 - D) + 2D = 34

 expanding, we get 44 - 4D + 2D = 34

 solving, we get D = 5. Therefore, G = 6

 Proof: (5 x 2) + (6 x 4) = 34