A farmer has some cows and hens. The total head count of all the hens and cows is 74 while the total leg count is 228. Find the number of hens?

Sure, let's solve this problem step by step.

Step 1: Let's denote the number of cows as C and the number of hens as H.

Step 2: From the problem, we know two things:

• The total number of heads (which is the same as the total number of animals) is 74. So, we have the equation C + H = 74.
• The total number of legs is 228. Since cows have 4 legs and hens have 2, we have another equation: 4C + 2H = 228.

Step 3: To make the equations easier to solve, let's simplify the second equation by dividing the whole equation by 2, which gives us 2C + H = 114.

Step 4: Now we have a system of two equations, and we can solve it by substitution or elimination. If we subtract the first equation (C + H = 74) from the modified second equation (2C + H = 114), we get C = 40.

Step 5: Substitute C = 40 into the first equation, we get 40 + H = 74, which gives H = 34.

So, the farmer has 34 hens.