Question

A farmhouse shelters 11 animals. Some are goats and some are ducks. Altogether there are 34 legs. How many of each animal are there?

Answer 1

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