In a group of goats and hens, the number of legs is 12 more than twice the number of heads. The number of goats is _______?
In a group of goats and hens, the number of legs is 12 more than twice the number of heads. The number of goats is _______?
Explanation
Let's denote the number of goats as G and the number of hens as H.
Each goat has 1 head and 4 legs. Each hen has 1 head and 2 legs.
Number of heads = G + H
Number of legs = 4G + 2H
Given:
Number of legs = 2 × Number of heads + 12
4G + 2H = 2(G + H) + 12
Simplify:
4G + 2H = 2G + 2H + 12
4G - 2G = 12
2G = 12
G = 6