A group of 280 animals are on a farm. For each dog, there are three sheep. For each sheep, there are three horses. For each horse, there are three cows. How many horses are on the farm?
Question
A group of 280 animals are on a farm. For each dog, there are three sheep. For each sheep, there are three horses. For each horse, there are three cows. How many horses are on the farm?
Solution
Let's break down the problem:
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We know that for each dog, there are three sheep. Let's denote the number of dogs as D, the number of sheep as S, the number of horses as H, and the number of cows as C.
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From the problem, we know that S = 3D, H = 3S, and C = 3H.
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We also know that the total number of animals is 280, so D + S + H + C = 280.
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We can substitute the equations from step 2 into the equation from step 3 to get D + 3D + 9D + 27D = 280.
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Simplifying this equation gives 40D = 280.
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Solving for D, we find that D = 7.
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Substituting D = 7 into the equation H = 3S = 9D, we find that H = 63.
So, there are 63 horses on the farm.
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