Question

A farm has cows and ducks. There are 78 feet and 27 heads. How many of each animal are there? How do you know?

Answer 1

`one\ cow\ has\ 4\ legs \ \ \ and\ \ \ one\ duck\ has\ 2\ legs\\\\c\ \rightarrow\ the\ number\ of\ the\ cows\\d\ \rightarrow\ the\ number\ of\ the\ ducks\\\\78\ feet\ \ \ \Rightarrow\ \ \ 4c+2d=78\\ 27\ heads\ \ \ \Rightarrow\ \ \ c+d=27\\\\ \left \{ {\big{4c+2d=78\ /:2\ \ } \atop \big{c+d=27\ /\cdot(-1)}} \right. \\\\ \left \{ {\big{2c+d=39\ \ } \atop \big{-c-d=-27}} \right. \\--------\\c=12\\\\c+d=27\ \ \ \Rightarrow\ \ \ d=27-12=15\\\\Ans.\ 12\ cows\ \ and\ \ 15\ ducks`