In a group of goats and hens, the total number of legs is 12 more than twice the total number ofheads. The number of goats

Let's solve the problem step by step:

Step 1: Let's assume the number of goats in the group is "g" and the number of hens is "h".

Step 2: Each goat has 4 legs, so the total number of goat legs is 4g.

Step 3: Each hen has 2 legs, so the total number of hen legs is 2h.

Step 4: The total number of legs in the group is the sum of goat legs and hen legs, which is 4g + 2h.

Step 5: The total number of heads in the group is the sum of goats and hens, which is g + h.

Step 6: According to the problem, the total number of legs is 12 more than twice the total number of heads. Mathematically, this can be represented as:

4g + 2h = 2(g + h) + 12

Step 7: Simplifying the equation, we get:

4g + 2h = 2g + 2h + 12

Step 8: Combining like terms, we have:

2g = 12

Step 9: Dividing both sides of the equation by 2, we find:

g = 6

Step 10: Therefore, the number of goats in the group is 6.