can you solve the word problem? chickens and rabbits are placed in the same cage. there are 35 heads and 94 feet. how many chickens and rabbits are there?

Answer 1

To solve this problem, we can use a system of equations. Let's denote:

• \( c \) = number of chickens
• \( r \) = number of rabbits

We know the following:

1. Each chicken and rabbit has one head, and there are a total of 35 heads. This gives us our first equation: \[ c + r = 35 \]

2. Chickens have 2 feet, and rabbits have 4 feet. The total number of feet is 94, which gives us our second equation: \[ 2c + 4r = 94 \]

Now we can solve this system of equations.

First, we simplify the second equation. We can divide the entire equation by 2: \[ c + 2r = 47 \]

Now, we have the following system of equations:

1. \( c + r = 35 \)
2. \( c + 2r = 47 \)

Next, we can subtract the first equation from the second: \[ (c + 2r) - (c + r) = 47 - 35 \] This simplifies to: \[ r = 12 \]

Now that we know there are 12 rabbits, we can substitute \( r \) back into the first equation to find \( c \): \[ c + 12 = 35 \] \[ c = 35 - 12 = 23 \]

Therefore, the solution to the problem is:

• Number of chickens = 23
• Number of rabbits = 12

In conclusion:

• There are 23 chickens and 12 rabbits.