There are 36 chickens and dogs in the cage, with a total of 100 legs. How many chickens and dogs are there
number of chickens --- x
number of dogs ------36-x
solve for x....
2x + 4(36-x) = 100
To determine the number of chickens and dogs in the cage, we can use a system of equations. Let's assign variables to the unknowns:
Let 'c' represent the number of chickens.
Let 'd' represent the number of dogs.
From the given information, we know that the total number of chickens and dogs is 36:
c + d = 36 ------ Equation 1
We also know that the total number of legs is 100. Since each chicken has 2 legs and each dog has 4 legs, we can create another equation:
2c + 4d = 100 ------ Equation 2
Now, we have a system of equations. We can solve them simultaneously to find the values of 'c' and 'd'.
We can simplify Equation 1 by isolating 'c':
c = 36 - d
Substituting this value of 'c' into Equation 2:
2(36 - d) + 4d = 100
Expanding and simplifying:
72 - 2d + 4d = 100
Combining like terms:
2d = 100 - 72
2d = 28
Dividing both sides by 2:
d = 28 / 2
d = 14
Now that we have found the value of 'd', we can substitute it back into Equation 1 to find 'c':
c + 14 = 36
Subtracting 14 from both sides:
c = 36 - 14
c = 22
Therefore, there are 22 chickens and 14 dogs in the cage.