Question

The number of dogs and chickens on a farm add up to 12. The number of legs between them is 30. How many dogs and how many chickens are on the farm if there are at least twice as many chickens as dogs?

Answer 1

By setting up a system of equations and solving them, we find that the farm has 3 dogs and 9 chickens, which satisfies the given conditions.

Step-by-step explanation:

To solve the problem of determining the number of dogs and chickens on a farm, where the total number of animals is 12 and the total number of legs is 30, with at least twice as many chickens as dogs, we can use a system of equations.

Let's define two variables: D for the number of dogs and C for the number of chickens.

The first equation comes from the total number of animals: D + C = 12.

The second equation comes from the total number of legs: 4D + 2C = 30 (because dogs have 4 legs and chickens have 2 legs).

The condition given is that there are at least twice as many chickens as dogs, which can be expressed as: C ≥ 2D.

Now, let's solve this system. By multiplying the first equation by 2, we get 2D + 2C = 24. If we subtract the second equation from this, we get 2D + 2C - (4D + 2C) = 24 - 30, which simplifies to -2D = -6, therefore D = 3.

Using D = 3 in the first equation, we get 3 + C = 12, and solving for C gives us C = 9.

So, the farm has 3 dogs and 9 chickens, which satisfies all the conditions of the problem.