lets
h =# of hens in the filed and c = # of cows in the field
hens and cows have 50 heads
h + c = 50 (1)
hens and cows have 180 legs (hen has 2 legs and cow has 4 legs)
2h + 4c = 180 (2)
From equation (1) h + c = 50 ----> h = 50 - c
substitute h = 50 - c into 2h + 4c = 180 (
2h + 4c =180
2(50 - c) + 4c = 180
100 - 2c + 4c = 180
2c = 180 - 100
2c = 80
c = 40
2h + 4(40) = 180
2h + 160 = 180
2h = 20
h = 10
answer
hens = 10 and cows = 40
double check:
heads: 10 hens + 40 cows = 50 total
legs:10(2) + 40(4) = 20 + 160 = 180
