how many of each animal does farmer johnson have?

Question

Johnsons farming operation has both cattle and chickens. One day a farmer Johnson was gazing into the eyes of his cattle and chickens he noticed there were 162 eyes and 258 total legs. How many two legged chicken and 4 legged cattle does farmer johnson have?

Answer 1

Let x=number of cattle and y=number of chickens. Total number of legs=4x+2y=258, 2x+y=129; total number of eyes=2x+2y=162. x+y=81 so y=81-x; 2x+y=2x+81-x=129; x=129-81=48, so y=81-48=33. The number of cattle is 48 and the number of chickens is 33. Number of legs=4*48+2*33=192+66=258; number of eyes is 2*(48+33)=162.