There are some chickens and goats in a farm. The number of chickens is six times of the number of goats. The total number of legs of chickens is 112 more than the total number of legs of goats. How many goats are there?

Let's denote the number of goats as \( x \).

- Since the number of chickens is six times the number of goats, the number of chickens will be \( 6x \).
- Each goat has 4 legs, so the total number of legs of the goats is \( 4x \).
- Each chicken also has 2 legs, so the total number of legs of the chickens is \( 2(6x) = 12x \).
- According to the problem, the total number of chicken legs is 112 more than the total number of goat legs. Therefore, the equation is:

\[
12x = 4x + 112
\]

Now, let's solve the equation:

\[
12x - 4x = 112
\]

\[
8x = 112
\]

\[
x = \frac{112}{8} = 14
\]

Thus, the number of goats is \( \boxed{14} \).

Would you like more details or further clarification?

Here are 5 related questions for practice:
1. If the number of chickens was 5 times the number of goats, how would the equation change?
2. What would happen if each chicken had 4 legs and each goat had 2 legs?
3. How many chickens are there if the number of goats is 14?
4. How many total animals are there in the farm?
5. How many total legs are there for all the animals combined?

**Tip:** When setting up word problems, clearly define variables and write out relationships step by step to avoid confusion.

There are some chickens and goats in a farm. The number of chickens is six times the number of goats. The total number of legs of chickens is 112 more than the total number of legs of goats. How many goats are there?

In this word problem, learn how to solve an algebraic equation involving the number of chickens and goats on a farm. The solution covers key concepts like forming linear equations and basic algebraic manipulation. Suitable for students in Grades 6-8.

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