Farmer Tom raises ducks and horses on his farm. All of his horses need new horseshoes. He calls the farrier (a person who puts shoes on horses) but has a difficult time remembering how many of each animal he owns. He knows that there are a total of 24 animals. The animals have a total of 62 legs (all animals have either two or four legs). How many horses does Tom own?
Let's say the number of horses is h and the number of ducks is d
Since all the animals have either two or four legs, the number of horse legs is 4h, and the number of duck legs is 2d.
We also know that there are a total of 24 animals, so h + d = 24 --- Equation (1)
The total number of legs is 62, so 4h + 2d = 62 --- Equation (2)
We can solve equations (1) and (2) simultaneously
Multiplying equation (1) by 2 gives 2h + 2d = 48
Subtracting this result from equation (2) gives 2h = 14
Dividing both sides by 2 gives h = 7
Therefore, Farmer Tom owns 7 horses. Answer: \boxed{7}.
Let's assume that Farmer Tom owns 'x' horses and 'y' ducks.
1. Total number of animals: x + y = 24
2. Total number of legs: 4x + 2y = 62
To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the method of substitution:
From equation 1, we can express x in terms of y as:
x = 24 - y
Substituting this value of x into equation 2:
4(24 - y) + 2y = 62
96 - 4y + 2y = 62
96 - 2y = 62
-2y = 62 - 96
-2y = -34
y = -34 / -2
y = 17
Now, we can substitute the value of y back into equation 1 to find the number of horses:
x = 24 - 17
x = 7
Therefore, Farmer Tom owns 7 horses.
If you have any further questions, feel free to ask.