Question

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.