A farmer has chickens and cows. If there are 20 heads and 56 legs in total, how

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Question: A farmer has chickens and cows. If there are 20 heads and 56 legs in total, how many cows are there?

Options:

Correct Answer: 10

Solution:

Let the number of chickens be c and the number of cows be k. We have the equations: c + k = 20 and 2c + 4k = 56. Solving these gives k = 10.

A farmer has chickens and cows. If there are 20 heads and 56 legs in total, how many cows are there?

A farmer has chickens and cows. If there are 20 heads and 56 legs in total, how many cows are there?

Step 1: Understand that each chicken has 1 head and each cow has 1 head. So, if we count all the heads, we can say the total number of chickens (c) plus the total number of cows (k) equals 20. This gives us the equation: c + k = 20.
Step 2: Next, we know that each chicken has 2 legs and each cow has 4 legs. So, if we count all the legs, we can say 2 times the number of chickens (2c) plus 4 times the number of cows (4k) equals 56. This gives us the second equation: 2c + 4k = 56.
Step 3: Now we have two equations: c + k = 20 and 2c + 4k = 56. We can use the first equation to express c in terms of k. From c + k = 20, we can rearrange it to c = 20 - k.
Step 4: Substitute c = 20 - k into the second equation (2c + 4k = 56). This gives us 2(20 - k) + 4k = 56.
Step 5: Simplify the equation: 40 - 2k + 4k = 56. Combine like terms to get 40 + 2k = 56.
Step 6: Now, subtract 40 from both sides: 2k = 16.
Step 7: Divide both sides by 2 to find k: k = 8. This means there are 8 cows.
Step 8: To find the number of chickens, substitute k back into the first equation: c + 8 = 20, so c = 12. This means there are 12 chickens.

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