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.