There are 12 animals in a farm.some are cows the rest are chickens.there are 28 animals legs in all.how many cows are there? how many chickens are there ?
cows --- x
chickesn --- y
x+y = 12 **
4x + 2y = 28 or 2x + y = 14 ***
subtract ** from ***
x = 2
then y = 10
2 cows and 10 chicks
2 cows and 10 chikens
Let's solve this step-by-step. Let's denote the number of cows as "C" and the number of chickens as "Ch."
Step 1: Write down the given information:
- There are 12 animals in total.
- Some of these animals are cows.
- The rest of the animals are chickens.
- There are a total of 28 animal legs.
Step 2: Determine the number of legs for each type of animal:
- Cows have 4 legs.
- Chickens have 2 legs.
Step 3: Form equations based on the given information:
- The total number of animals: C + Ch = 12 (Equation 1)
- The total number of legs: 4C + 2Ch = 28 (Equation 2)
Step 4: Solve the equations:
Using Equation 1, we can express C in terms of Ch: C = 12 - Ch.
Substituting this value of C into Equation 2:
4(12 - Ch) + 2Ch = 28
48 - 4Ch + 2Ch = 28
48 - 28 = 4Ch - 2Ch
20 = 2Ch
Ch = 20 / 2
Ch = 10
Step 5: Determine the number of cows:
Using Equation 1: C = 12 - Ch
C = 12 - 10
C = 2
So, there are 2 cows and 10 chickens in the farm.
To find the number of cows and chickens, we can use a system of equations based on the information given.
Let's assume that the number of cows is represented by 'C' and the number of chickens is represented by 'Ch'.
1) The first equation is based on the total number of animals: C + Ch = 12
2) The second equation is based on the total number of legs: 4C + 2Ch = 28
Now, we can solve these equations simultaneously to find the values of C and Ch.
To do that, we can solve equation (1) for C: C = 12 - Ch
Substituting this value of C into equation (2), we get:
4(12 - Ch) + 2Ch = 28
Simplifying the equation:
48 - 4Ch + 2Ch = 28
-2Ch = 28 - 48
-2Ch = -20
Now, divide both sides of the equation by -2:
Ch = -20 / -2
Ch = 10
So, there are 10 chickens on the farm.
To find the number of cows, we can substitute the value of Ch into equation (1):
C + 10 = 12
Subtracting 10 from both sides of the equation:
C = 12 - 10
C = 2
Therefore, there are 2 cows on the farm.