Question

A farmer has 30 chickens and rabbits altogether. There are 100 legs. How many chickens does the farmer have?

A) 15 chickens
B) 20 chickens
C) 25 chickens
D) 30 chickens

Answer 1

By setting up a system of equations with the variables C for chickens and R for rabbits, we can find that the farmer has 10 chickens, which does not match any of the given options A, B, C, or D.

Step-by-step explanation:

To find out how many chickens the farmer has, let's use a system of equations based on the given information. We have a total of 30 animals, which are a mix of chickens and rabbits. Chickens have 2 legs each, while rabbits have 4 legs each.

Let's assign the variable C to represent the number of chickens and R to represent the number of rabbits. We can then set up the following two equations based on the information given:

1. C + R = 30 (total number of chickens and rabbits)
2. 2C + 4R = 100 (total number of legs)

We can solve this system of equations by multiplying the first equation by 2, getting 2C + 2R = 60, and then subtracting this from the second equation to eliminate C:

2C + 4R = 100
- (2C + 2R = 60)

This simplifies to:

2R = 40

Dividing through by 2 gives us:

R = 20

Now we substitute the value of R back into the first equation:

C + 20 = 30

Which gives us:

C = 10

Therefore, the farmer has 10 chickens and 20 rabbits. Since none of the options A, B, C, or D are correct, there seems to be an error in the question or the options provided.