In a farm, the farmer counted 78 legs and 35 heads consisting of cows and hens. How many hens does he have?
4 c + 2 h = 78
c+h = 35 so 2h = 70-2c
4 c + 70 - 2c = 78
2 c = 8
c = 4
35 - 4 = 31 hens
In a farm a man counted his goats and hens .In all he had 30 legs and 13 heads.how many goats are in the farm and how many hens are in the farm
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Well, let's put our thinking cap on and try to solve this riddle! Now, we know that cows have 4 legs and 1 head, while hens have 2 legs and 1 head. So, if we break this down, we have a total of 78 legs. If all the animals were cows, we would have 78/4 = 19.5 cows. And since we can't have half a cow (that would just be udderly ridiculous!), we can safely assume that there are some hens in the mix.
Now, let's move on to the number of heads. We have a total of 35 heads. If all the animals were hens, we would have 35/1 = 35 hens. But since we know there are cows, we can subtract the number of cows from the total number of animals (35 - 19.5 = 15.5). Now, since we can't have half a hen either (that would just be clucking madness!), we can conclude that there are 15 hens on the farm.
So, to answer your question, the farmer has 15 hens on the farm!
To determine the number of hens, we need to use the information given about the number of legs and heads. Here's how we can do it:
1. Identify the number of legs each animal type has:
- Cows have 4 legs.
- Hens have 2 legs.
2. Calculate the total number of legs:
- Multiply the number of cows by 4.
- Multiply the number of hens by 2.
Let's assume the number of cows is C, and the number of hens is H:
- Total legs = (4 * C) + (2 * H) = 78 legs.
3. Identify the number of heads for each animal type:
- Cows have 1 head.
- Hens also have 1 head.
4. Calculate the total number of heads:
- Multiply the number of cows by 1.
- Multiply the number of hens by 1.
- Total heads = (1 * C) + (1 * H) = 35 heads.
Now, we have a system of two equations:
4C + 2H = 78 (equation 1)
C + H = 35 (equation 2)
From equation 2, we can express C in terms of H:
C = 35 - H
Substitute this expression for C in equation 1:
4(35 - H) + 2H = 78
Simplifying the equation:
140 - 4H + 2H = 78
-2H = -62
H = -62 / -2
H = 31
Therefore, the farmer has 31 hens on the farm.