A farmer has some hens and cows the total number of feet us 128 if the total number of of animals are 40 find how many hens and cows are there?
2H+4C=128
H+C=40
double the lower equation, then subtract the second equation from the first.
(2-2)H+4C-2C=128-80
2C=48
C=24
H=16
suppose there were
40 cows = 160 feet
so, you would need 32/2 = 16 fewer cows: 24. The 32 feet would be made up with 16 hens.
Let's solve this step-by-step:
Step 1: Assign variables
Let's assume the number of hens as 'x' and the number of cows as 'y'.
Step 2: Formulate equations
From the given information, we know that each hen has 2 feet and each cow has 4 feet. We also know that the total number of animals is 40 and the total number of feet is 128. We can use this information to form two equations:
Equation 1: x + y = 40 (total number of animals)
Equation 2: 2x + 4y = 128 (total number of feet)
Step 3: Solve the equations
To solve these equations, we can use the substitution method.
First, solve equation 1 for x:
x = 40 - y
Then substitute this value of x into equation 2:
2(40 - y) + 4y = 128
Simplify the equation:
80 - 2y + 4y = 128
80 + 2y = 128
2y = 128 - 80
2y = 48
y = 48/2
y = 24
Now substitute the value of y back into equation 1 to find x:
x + 24 = 40
x = 40 - 24
x = 16
Step 4: Find the solution
Therefore, there are 16 hens and 24 cows on the farm.
To find the number of hens and cows, we can set up a system of equations. Let's use variables to represent the number of hens and cows.
Let h represent the number of hens and c represent the number of cows.
We are given two pieces of information:
1. The total number of animals is 40: h + c = 40.
2. The total number of feet is 128: 2h + 4c = 128 (since each hen has 2 feet and each cow has 4 feet).
We can solve this system of equations to find the values of h and c.
Using the first equation, we can isolate one variable:
h = 40 - c.
Now, substitute this value of h into the second equation:
2(40 - c) + 4c = 128.
Expand and solve for c:
80 - 2c + 4c = 128,
2c = 48,
c = 24.
Now, substitute the value of c back into the equation h = 40 - c:
h = 40 - 24,
h = 16.
Therefore, there are 16 hens and 24 cows.