There are 7 more cows than chickens on a farm. If there is a total of 160 legs, how many chickens are there?

Let's solve this problem using algebra.

1. **Define the variables:**
   - Let \( c \) represent the number of chickens.
   - Let \( k \) represent the number of cows.

2. **Set up the equations:**
   - According to the problem, there are 7 more cows than chickens:
     \[
     k = c + 7
     \]
   - Chickens have 2 legs each, and cows have 4 legs each. The total number of legs is given as 160. Thus, we can write the equation for the total number of legs:
     \[
     2c + 4k = 160
     \]

3. **Substitute the first equation into the second:**
   - Replace \( k \) in the second equation with \( c + 7 \):
     \[
     2c + 4(c + 7) = 160
     \]

4. **Simplify and solve for \( c \):**
   - Distribute and combine like terms:
     \[
     2c + 4c + 28 = 160
     \]
     \[
     6c + 28 = 160
     \]
   - Subtract 28 from both sides:
     \[
     6c = 132
     \]
   - Divide both sides by 6:
     \[
     c = 22
     \]

So, there are **22 chickens** on the farm.

5. **Find the number of cows to verify:**
   - Using \( k = c + 7 \):
     \[
     k = 22 + 7 = 29
     \]

6. **Verify the solution by checking the total number of legs:**
   - Chickens: \( 22 \times 2 = 44 \) legs.
   - Cows: \( 29 \times 4 = 116 \) legs.
   - Total legs: \( 44 + 116 = 160 \).

The calculation matches the problem's condition. Hence, the solution is verified.

### Do you have any questions or would you like further details?

### Relative Questions:
1. How many cows are there on the farm?
2. If there were 10 more animals (either cows or chickens), how many legs would there be in total?
3. If each cow has 5 legs (hypothetically), how would that change the total number of legs?
4. What would be the total number of legs if there were twice as many cows as chickens?
5. How many chickens and cows are there if the total number of legs is 200?

### Tip:
When dealing with word problems involving numbers, defining variables and setting up equations based on given relationships and conditions can simplify the process of finding the solution.

Learn how to solve a word problem involving chickens and cows on a farm. This problem requires setting up equations based on given relationships and conditions, calculating total legs, and verifying the solution. Suitable for students in Grades 7-9.

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