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