Question

at the fair the chickens and the rabbits were placed under the same tent the chickens and the rabbits have a total of 360 legs if there were 105 animals how many were rabbits

Answer 1

Let \( c \) represent the number of chickens and \( r \) represent the number of rabbits. We can set up the following equations based on the information provided:

1. The total number of animals (chickens and rabbits) is 105:
\[
c + r = 105
\]

2. The total number of legs (chickens have 2 legs and rabbits have 4 legs) is 360:
\[
2c + 4r = 360
\]

We can simplify the second equation by dividing everything by 2:
\[
c + 2r = 180
\]

Now we have a system of equations:
1. \( c + r = 105 \) (Equation 1)
2. \( c + 2r = 180 \) (Equation 2)

Next, we can solve these equations. We can subtract Equation 1 from Equation 2:
\[
(c + 2r) - (c + r) = 180 - 105
\]
\[
r = 75
\]

Now that we have \( r \), we can find \( c \) using Equation 1:
\[
c + 75 = 105
\]
\[
c = 105 - 75 = 30
\]

So, the number of rabbits is \( r = 75 \).

Thus, there are **75 rabbits**.