There are 13 animals in the barn. Some are chickens and some are sheep. There are 32 legs in all. How many of each animal are there?
2 legs per animal yields 26 legs
There are 6 extra legs, so what does that say? Think about what happens when you replace a chicken with a sheep.
To find out how many of each animal are in the barn, we can set up a system of equations based on the information given. Let's use variables to represent the number of chickens and sheep.
Let's say the number of chickens is represented by 'c', and the number of sheep is represented by 's'.
From the given information, we know that there are 13 animals in total:
c + s = 13 --- Equation 1
And we also know that there are 32 legs in total:
2c + 4s = 32 --- Equation 2
Now we have a system of equations to solve simultaneously. There are several methods to do this, but I'll explain one method called substitution:
1. Solve Equation 1 for 'c':
c = 13 - s
2. Substitute this value of 'c' into Equation 2:
2(13 - s) + 4s = 32
3. Simplify and solve for 's':
26 - 2s + 4s = 32
2s = 6
s = 3
4. Substitute the value of 's' back into Equation 1 to find 'c':
c + 3 = 13
c = 13 - 3
c = 10
Therefore, there are 10 chickens and 3 sheep in the barn.